Details

analyze1.6s (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample179.0ms (0.1%)

Algorithm

1×

intervals

Results

104.0ms	126×	body	2048	valid
31.0ms	84×	body	1024	valid
7.0ms	310×	pre	128	true
6.0ms	14×	body	2048	overflowed
5.0ms	23×	body	512	valid
5.0ms	17×	body	1024	overflowed
2.0ms	12×	body	256	valid
2.0ms	8×	body	512	overflowed
1.0ms	11×	body	128	valid
1.0ms	5×	body	256	overflowed
1.0ms	10×	body	128	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify109.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5217	37

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

61.8b

Counts

2 → 1

Compiler

Compiled 24 to 19 computations (20.8% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

2.7b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
0.7b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(*.f64 (+.f64 a b) eps)
0.7b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.7b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
2.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1123`
26×	`*-un-lft-identity_binary64_1101`
15×	`cancel-sign-sub-inv_binary64_1067`
11×	`add-cube-cbrt_binary64_1136`
10×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140`
9×	`flip--_binary64_1076` `flip3--_binary64_1105`
7×	`associate-r_binary64_1041` `associate-l_binary64_1042`
6×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
5×	`sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053`
4×	`frac-times_binary64_1111` `distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
3×	`diff-log_binary64_1193`
2×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069`

Counts

4 → 96

Calls

8 calls:

13.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
0.0ms	(*.f64 (+.f64 a b) eps)

series360.0ms (0.3%)

Counts

4 → 41

Calls

4 calls:

181.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
63.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
58.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
58.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

Compiler

Compiled 2138 to 1636 computations (23.5% saved)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5010	2533

prune513.0ms (0.4%)

Pruning

41 alts after pruning (40 fresh and 1 done)

	Pruned	Kept	Total
New	97	40	137
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	97	41	138

Error

47.7b

Counts

138 → 41

Compiler

Compiled 4012 to 2062 computations (48.6% saved)

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b	(.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))) (-.f64 (exp.f64 (.f64 b eps)) 1))
0.2b	(.f64 1/2 (.f64 a a))
0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(*.f64 (+.f64 a b) eps)
2.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
3.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
6.7b	(.f64 eps (.f64 1/2 (*.f64 a a)))

rewrite51.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
15×	`add-sqr-sqrt_binary64_1123` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
13×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162`
10×	`associate-*r/_binary64_1043`
8×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
7×	`add-cube-cbrt_binary64_1136`
6×	`flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067`
4×	`difference-of-squares_binary64_1070` `frac-times_binary64_1111`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-l_binary64_1042`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `associate-/l/_binary64_1048` `associate-*l/_binary64_1044`
1×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l_binary64_1046` `times-frac_binary64_1107` `associate-r_binary64_1041` `associate-/r*_binary64_1045`

Counts

4 → 92

Calls

8 calls:

21.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
6.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
0.0ms	(*.f64 (+.f64 a b) eps)

series920.0ms (0.7%)

Counts

4 → 38

Calls

4 calls:

714.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
91.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
71.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
44.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

Compiler

Compiled 3173 to 2217 computations (30.1% saved)

simplify113.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4988	3180
1	4988	3180

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

4.3b	(.f64 a (.f64 b (*.f64 eps eps)))
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(*.f64 (+.f64 a b) eps)
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.3b	(.f64 a (.f64 b (*.f64 eps eps)))
8.5b	(.f64 b (.f64 eps eps))
38.3b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 a (.f64 b (*.f64 eps eps))))

rewrite44.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
25×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
18×	`pow1_binary64_1162`
12×	`add-sqr-sqrt_binary64_1123`
10×	`*-un-lft-identity_binary64_1101`
9×	`pow-prod-down_binary64_1172`
8×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
7×	`add-cube-cbrt_binary64_1136`
6×	`add-log-exp_binary64_1140` `associate-l_binary64_1042`
3×	`cancel-sign-sub-inv_binary64_1067`
2×	`-commutative_binary64_1032` `difference-of-squares_binary64_1070` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-r/_binary64_1043` `associate-r_binary64_1041`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `clear-num_binary64_1100` `distribute-lft-out--_binary64_1053` `div-inv_binary64_1098` `associate-/l_binary64_1046` `times-frac_binary64_1107` `unswap-sqr_binary64_1069` `associate-/r_binary64_1045`

Counts

4 → 89

Calls

8 calls:

15.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 a (.f64 b (*.f64 eps eps))))
8.0ms	(.f64 a (.f64 b (*.f64 eps eps)))
6.0ms	(.f64 b (.f64 eps eps))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
0.0ms	(*.f64 (+.f64 a b) eps)

series489.0ms (0.4%)

Counts

4 → 38

Calls

4 calls:

230.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 a (.f64 b (*.f64 eps eps))))
126.0ms	(.f64 a (.f64 b (*.f64 eps eps)))
71.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
62.0ms	(.f64 b (.f64 eps eps))

Compiler

Compiled 1393 to 1007 computations (27.7% saved)

simplify55.0ms (0%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5047	2066

localize32.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(*.f64 (+.f64 a b) eps)
0.0b	(+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3))))))
0.0b	(.f64 1/2 (.f64 eps eps))
2.7b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))))
3.1b	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
14.6b	(.f64 (.f64 b b) (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3)))))

rewrite50.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64_1139`
20×	`add-sqr-sqrt_binary64_1123`
16×	`add-cbrt-cube_binary64_1137`
15×	`*-un-lft-identity_binary64_1101`
13×	`pow1_binary64_1162`
11×	`prod-exp_binary64_1150` `associate-l_binary64_1042`
9×	`add-cube-cbrt_binary64_1136`
7×	`cbrt-unprod_binary64_1134` `associate-r_binary64_1041`
6×	`add-log-exp_binary64_1140`
5×	`pow-prod-down_binary64_1172`
4×	`difference-of-squares_binary64_1070` `frac-times_binary64_1111` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-*r/_binary64_1043` `flip-+_binary64_1075`
3×	`*-commutative_binary64_1032` `cancel-sign-sub-inv_binary64_1067`
2×	`difference-of-sqr-1_binary64_1071` `distribute-lft-in_binary64_1050` `distribute-lft-out--_binary64_1053` `unswap-sqr_binary64_1069` `associate-*l/_binary64_1044` `distribute-rgt-in_binary64_1051`
1×	`diff-log_binary64_1193` `pow-exp_binary64_1169` `sub-neg_binary64_1094` `pow-to-exp_binary64_1170`

Counts

4 → 92

Calls

8 calls:

13.0ms	(.f64 (.f64 b b) (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3)))))
12.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))))
7.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
0.0ms	(.f64 1/2 (.f64 eps eps))

series885.0ms (0.7%)

Counts

4 → 45

Calls

4 calls:

564.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))))
121.0ms	(.f64 (.f64 b b) (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3)))))
102.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
98.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

Compiler

Compiled 3463 to 2504 computations (27.7% saved)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5009	4216

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (+.f64 1 (sqrt.f64 (exp.f64 (.f64 a eps)))) (+.f64 -1 (sqrt.f64 (exp.f64 (*.f64 a eps)))))
0.0b	(+.f64 1 (sqrt.f64 (exp.f64 (*.f64 a eps))))
0.0b	(sqrt.f64 (exp.f64 (*.f64 a eps)))
0.0b	(sqrt.f64 (exp.f64 (*.f64 a eps)))
0.7b	(.f64 (.f64 (+.f64 1 (sqrt.f64 (exp.f64 (.f64 a eps)))) (+.f64 -1 (sqrt.f64 (exp.f64 (.f64 a eps))))) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.7b	(+.f64 -1 (sqrt.f64 (exp.f64 (*.f64 a eps))))
2.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`frac-times_binary64_1111`
21×	`add-sqr-sqrt_binary64_1123`
20×	`*-un-lft-identity_binary64_1101`
19×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
14×	`associate-*l/_binary64_1044`
12×	`cancel-sign-sub-inv_binary64_1067`
11×	`flip--_binary64_1076` `flip3--_binary64_1105`
10×	`add-log-exp_binary64_1140`
9×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
8×	`associate-*r/_binary64_1043`
7×	`associate-r_binary64_1041`
6×	`difference-of-squares_binary64_1070`
4×	`sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `pow-prod-down_binary64_1172`
2×	`diff-log_binary64_1193`
1×	`-commutative_binary64_1032` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `+-commutative_binary64_1031` `associate-l*_binary64_1042`

Counts

4 → 104

Calls

8 calls:

18.0ms	(.f64 (.f64 (+.f64 1 (sqrt.f64 (exp.f64 (.f64 a eps)))) (+.f64 -1 (sqrt.f64 (exp.f64 (.f64 a eps))))) (-.f64 (exp.f64 (*.f64 b eps)) 1))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 (*.f64 a eps))))
5.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
0.0ms	(sqrt.f64 (exp.f64 (*.f64 a eps)))

series527.0ms (0.4%)

Counts

4 → 39

Calls

4 calls:

329.0ms	(.f64 (.f64 (+.f64 1 (sqrt.f64 (exp.f64 (.f64 a eps)))) (+.f64 -1 (sqrt.f64 (exp.f64 (.f64 a eps))))) (-.f64 (exp.f64 (*.f64 b eps)) 1))
71.0ms	(+.f64 -1 (sqrt.f64 (exp.f64 (*.f64 a eps))))
69.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
58.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

Compiler

Compiled 2582 to 1814 computations (29.7% saved)

simplify94.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5084	3568

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(*.f64 (+.f64 a b) eps)
0.0b	(/.f64 (.f64 (+.f64 -1 (pow.f64 (exp.f64 (.f64 b eps)) 3)) (+.f64 -1 (exp.f64 (.f64 a eps)))) (+.f64 (.f64 (exp.f64 (.f64 b eps)) (exp.f64 (.f64 b eps))) (+.f64 (.f64 1 1) (.f64 (exp.f64 (*.f64 b eps)) 1))))
0.0b	(+.f64 (.f64 (exp.f64 (.f64 b eps)) (exp.f64 (.f64 b eps))) (+.f64 (.f64 1 1) (.f64 (exp.f64 (.f64 b eps)) 1)))
0.5b	(.f64 (+.f64 -1 (pow.f64 (exp.f64 (.f64 b eps)) 3)) (+.f64 -1 (exp.f64 (*.f64 a eps))))
2.7b	(+.f64 -1 (exp.f64 (*.f64 a eps)))
2.9b	(+.f64 -1 (pow.f64 (exp.f64 (*.f64 b eps)) 3))
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_1101`
13×	`add-sqr-sqrt_binary64_1123`
10×	`add-log-exp_binary64_1140`
8×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
7×	`add-cube-cbrt_binary64_1136`
6×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
4×	`frac-times_binary64_1111` `distribute-lft-out_binary64_1052` `associate-r_binary64_1041` `associate-l_binary64_1042`
3×	`cancel-sign-sub-inv_binary64_1067`
2×	`difference-of-squares_binary64_1070` `sum-log_binary64_1192` `associate-r/_binary64_1043` `+-commutative_binary64_1031` `associate-l/_binary64_1044`
1×	`diff-log_binary64_1193` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-in_binary64_1050` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051`

Counts

4 → 72

Calls

8 calls:

13.0ms	(.f64 (+.f64 -1 (pow.f64 (exp.f64 (.f64 b eps)) 3)) (+.f64 -1 (exp.f64 (*.f64 a eps))))
6.0ms	(+.f64 -1 (pow.f64 (exp.f64 (*.f64 b eps)) 3))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(+.f64 -1 (exp.f64 (*.f64 a eps)))
0.0ms	(+.f64 (.f64 (exp.f64 (.f64 b eps)) (exp.f64 (.f64 b eps))) (+.f64 (.f64 1 1) (.f64 (exp.f64 (.f64 b eps)) 1)))

series511.0ms (0.4%)

Counts

4 → 36

Calls

4 calls:

282.0ms	(.f64 (+.f64 -1 (pow.f64 (exp.f64 (.f64 b eps)) 3)) (+.f64 -1 (exp.f64 (*.f64 a eps))))
91.0ms	(+.f64 -1 (pow.f64 (exp.f64 (*.f64 b eps)) 3))
72.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
66.0ms	(+.f64 -1 (exp.f64 (*.f64 a eps)))

Compiler

Compiled 3409 to 2243 computations (34.2% saved)

simplify73.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4972	2161
1	4972	2161

prune13.5s (10.4%)

Pruning

268 alts after pruning (264 fresh and 4 done)

	Pruned	Kept	Total
New	409	236	645
Fresh	7	28	35
Picked	0	0	0
Done	2	4	6
Total	418	268	686

Error

0.1b

Counts

686 → 268

Compiler

Compiled 27529 to 14370 computations (47.8% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

13.2b	(/.f64 (+.f64 a b) (*.f64 a b))
13.2b	(/.f64 (+.f64 a b) (*.f64 a b))

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_1101`
6×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
4×	`associate-/l*_binary64_1046` `times-frac_binary64_1107`
3×	`add-sqr-sqrt_binary64_1123` `add-cube-cbrt_binary64_1136`
2×	`distribute-lft-out_binary64_1052` `associate-/l/_binary64_1048` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
1×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `pow1_binary64_1162` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `flip-+_binary64_1075` `associate-/r*_binary64_1045`

Counts

1 → 25

Calls

2 calls:

7.0ms	(/.f64 (+.f64 a b) (*.f64 a b))
0.0ms	(/.f64 (+.f64 a b) (*.f64 a b))

series107.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

107.0ms

(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 102 to 126 computations (-23.5% saved)

simplify55.0ms (0%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5070	408

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize22.0ms (0%)

Local error

Found 8 expressions with local error:

1.0b	(.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))) (-.f64 (exp.f64 (.f64 b eps)) 1))
0.2b	(.f64 1/2 (.f64 a a))
0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(*.f64 (+.f64 a b) eps)
2.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
3.7b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
6.7b	(.f64 eps (.f64 1/2 (*.f64 a a)))

rewrite48.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
15×	`add-sqr-sqrt_binary64_1123` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
13×	`*-un-lft-identity_binary64_1101` `pow1_binary64_1162`
10×	`associate-*r/_binary64_1043`
8×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
7×	`add-cube-cbrt_binary64_1136`
6×	`flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `cancel-sign-sub-inv_binary64_1067`
4×	`difference-of-squares_binary64_1070` `frac-times_binary64_1111`
3×	`flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-l_binary64_1042`
2×	`diff-log_binary64_1193` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `associate-/l/_binary64_1048` `associate-*l/_binary64_1044`
1×	`-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l_binary64_1046` `times-frac_binary64_1107` `associate-r_binary64_1041` `associate-/r*_binary64_1045`

Counts

4 → 92

Calls

8 calls:

18.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
0.0ms	(*.f64 (+.f64 a b) eps)

series918.0ms (0.7%)

Counts

4 → 38

Calls

4 calls:

697.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 eps (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a))))) (-.f64 (exp.f64 (.f64 b eps)) 1)))
95.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
77.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
49.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

Compiler

Compiled 3309 to 2353 computations (28.9% saved)

simplify107.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4988	3180
1	4988	3180

localize36.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 (+.f64 a b) eps)
0.0b	(+.f64 (exp.f64 (*.f64 a eps)) 1)
0.0b	(+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3))))) eps)
0.0b	(.f64 1/2 (.f64 eps eps))
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
4.1b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (/.f64 (.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (+.f64 -1 (pow.f64 (exp.f64 a) (.f64 2 eps)))) (+.f64 (exp.f64 (*.f64 a eps)) 1)))
4.7b	(.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (+.f64 -1 (pow.f64 (exp.f64 a) (.f64 2 eps))))
7.8b	(.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))

rewrite84.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
21×	`*-un-lft-identity_binary64_1101`
18×	`add-sqr-sqrt_binary64_1123` `times-frac_binary64_1107`
14×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
12×	`associate-*r/_binary64_1043` `add-cube-cbrt_binary64_1136`
11×	`pow1_binary64_1162`
10×	`associate-/r*_binary64_1045`
9×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
7×	`associate-r_binary64_1041`
6×	`add-log-exp_binary64_1140`
5×	`associate-/r/_binary64_1047`
4×	`frac-times_binary64_1111` `pow-prod-down_binary64_1172` `associate-l_binary64_1042`
3×	`distribute-lft-out_binary64_1052` `div-inv_binary64_1098` `cancel-sign-sub-inv_binary64_1067`
2×	`-commutative_binary64_1032` `difference-of-squares_binary64_1070` `distribute-lft-in_binary64_1050` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-l/_binary64_1044` `distribute-rgt-in_binary64_1051`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `clear-num_binary64_1100` `distribute-lft-out--_binary64_1053` `associate-/l*_binary64_1046` `unswap-sqr_binary64_1069`

Counts

4 → 119

Calls

8 calls:

27.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (/.f64 (.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (+.f64 -1 (pow.f64 (exp.f64 a) (.f64 2 eps)))) (+.f64 (exp.f64 (*.f64 a eps)) 1)))
19.0ms	(.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (+.f64 -1 (pow.f64 (exp.f64 a) (.f64 2 eps))))
11.0ms	(.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
0.0ms	(.f64 1/2 (.f64 eps eps))

series3.8s (3%)

Counts

4 → 48

Calls

4 calls:

2.9s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (/.f64 (.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (+.f64 -1 (pow.f64 (exp.f64 a) (.f64 2 eps)))) (+.f64 (exp.f64 (*.f64 a eps)) 1)))
721.0ms	(.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (+.f64 -1 (pow.f64 (exp.f64 a) (.f64 2 eps))))
118.0ms	(.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))
85.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

Compiler

Compiled 8023 to 5543 computations (30.9% saved)

simplify120.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4969	9036
1	4969	9036

localize40.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (.f64 (cbrt.f64 (-.f64 (exp.f64 (.f64 a eps)) 1)) (cbrt.f64 (-.f64 (exp.f64 (.f64 a eps)) 1))) (.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (cbrt.f64 (+.f64 -1 (exp.f64 (.f64 eps a))))))
0.0b	(*.f64 (+.f64 a b) eps)
0.0b	(+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3))))) eps)
0.0b	(.f64 1/2 (.f64 eps eps))
2.7b	(.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (cbrt.f64 (+.f64 -1 (exp.f64 (.f64 eps a)))))
3.1b	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
3.7b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
7.8b	(.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))

rewrite56.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64_1139`
16×	`add-sqr-sqrt_binary64_1123`
15×	`*-un-lft-identity_binary64_1101`
14×	`add-cbrt-cube_binary64_1137`
13×	`pow1_binary64_1162`
11×	`prod-exp_binary64_1150` `associate-r_binary64_1041`
10×	`associate-*r/_binary64_1043` `add-cube-cbrt_binary64_1136`
7×	`cbrt-unprod_binary64_1134` `flip3-+_binary64_1104` `flip-+_binary64_1075` `associate-l_binary64_1042`
6×	`add-log-exp_binary64_1140` `cbrt-div_binary64_1133`
5×	`pow-prod-down_binary64_1172`
4×	`frac-times_binary64_1111` `cbrt-prod_binary64_1132`
3×	`*-commutative_binary64_1032` `cancel-sign-sub-inv_binary64_1067`
2×	`difference-of-squares_binary64_1070` `associate-*l/_binary64_1044`
1×	`diff-log_binary64_1193` `pow-exp_binary64_1169` `distribute-lft-out_binary64_1052` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-in_binary64_1050` `distribute-lft-out--_binary64_1053` `flip--_binary64_1076` `flip3--_binary64_1105` `unswap-sqr_binary64_1069` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051`

Counts

4 → 89

Calls

8 calls:

19.0ms	(.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (cbrt.f64 (+.f64 -1 (exp.f64 (.f64 eps a)))))
11.0ms	(.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))
7.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
0.0ms	(.f64 1/2 (.f64 eps eps))

series710.0ms (0.5%)

Counts

4 → 35

Calls

4 calls:

378.0ms	(.f64 (.f64 b (+.f64 (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))) eps)) (cbrt.f64 (+.f64 -1 (exp.f64 (.f64 eps a)))))
116.0ms	(.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))
111.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
104.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))

Compiler

Compiled 3750 to 2627 computations (29.9% saved)

simplify101.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4944	3105
1	4944	3105

prune20.3s (15.5%)

Pruning

469 alts after pruning (463 fresh and 6 done)

	Pruned	Kept	Total
New	246	212	458
Fresh	8	251	259
Picked	0	0	0
Done	3	6	9
Total	257	469	726

Error

0.1b

Counts

726 → 469

Compiler

Compiled 38345 to 23344 computations (39.1% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (/.f64 1 a) (/.f64 1 b))
0.0b	(+.f64 (/.f64 1 a) (/.f64 1 b))

rewrite15.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1101`
7×	`distribute-lft-out_binary64_1052`
6×	`times-frac_binary64_1107`
4×	`div-inv_binary64_1098`
3×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140` `add-cube-cbrt_binary64_1136`
1×	`sum-log_binary64_1192` `add-exp-log_binary64_1139` `pow1_binary64_1162` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `+-commutative_binary64_1031` `flip-+_binary64_1075` `frac-add_binary64_1109`

Counts

1 → 19

Calls

2 calls:

13.0ms	(+.f64 (/.f64 1 a) (/.f64 1 b))
0.0ms	(+.f64 (/.f64 1 a) (/.f64 1 b))

series58.0ms (0%)

Counts

1 → 12

Calls

1 calls:

58.0ms

(+.f64 (/.f64 1 a) (/.f64 1 b))

Compiler

Compiled 102 to 126 computations (-23.5% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4871	341
1	4871	341

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b	(exp.f64 (log.f64 (/.f64 (-.f64 (exp.f64 (.f64 eps (+.f64 a b))) 1) (.f64 (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))) (-.f64 (exp.f64 (.f64 eps b)) 1)))))
0.3b	(/.f64 (-.f64 (exp.f64 (.f64 eps (+.f64 a b))) 1) (.f64 (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))) (-.f64 (exp.f64 (.f64 eps b)) 1)))
0.2b	(.f64 1/2 (.f64 a a))
0.0b	(*.f64 eps (+.f64 a b))
2.5b	(.f64 (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))) (-.f64 (exp.f64 (*.f64 eps b)) 1))
2.9b	(-.f64 (exp.f64 (*.f64 eps b)) 1)
3.7b	(-.f64 (exp.f64 (*.f64 eps (+.f64 a b))) 1)
6.7b	(.f64 eps (.f64 1/2 (*.f64 a a)))

rewrite40.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_1123`
20×	`*-un-lft-identity_binary64_1101`
15×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
12×	`cancel-sign-sub-inv_binary64_1067`
11×	`add-cube-cbrt_binary64_1136`
8×	`add-log-exp_binary64_1140` `associate-r_binary64_1041`
7×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
6×	`difference-of-squares_binary64_1070` `associate-l_binary64_1042`
5×	`flip--_binary64_1076` `flip3--_binary64_1105`
4×	`frac-times_binary64_1111` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
3×	`difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053` `flip3-+_binary64_1104` `flip-+_binary64_1075`
2×	`diff-log_binary64_1193` `-commutative_binary64_1032` `associate-r/_binary64_1043` `associate-*l/_binary64_1044`
1×	`unswap-sqr_binary64_1069`

Counts

4 → 95

Calls

8 calls:

11.0ms	(.f64 (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))) (-.f64 (exp.f64 (*.f64 eps b)) 1))
8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
5.0ms	(-.f64 (exp.f64 (*.f64 eps (+.f64 a b))) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 eps b)) 1)
0.0ms	(*.f64 eps (+.f64 a b))

series488.0ms (0.4%)

Counts

4 → 42

Calls

4 calls:

270.0ms	(.f64 (+.f64 a (.f64 eps (.f64 1/2 (.f64 a a)))) (-.f64 (exp.f64 (*.f64 eps b)) 1))
93.0ms	(-.f64 (exp.f64 (*.f64 eps (+.f64 a b))) 1)
80.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
44.0ms	(-.f64 (exp.f64 (*.f64 eps b)) 1)

Compiler

Compiled 2384 to 1810 computations (24.1% saved)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4945	2727
1	4945	2727

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 1/2 (.f64 a a))
0.2b	(.f64 (.f64 (cbrt.f64 (.f64 eps (.f64 1/2 (.f64 a a)))) (cbrt.f64 (.f64 eps (.f64 1/2 (.f64 a a))))) (cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a)))))
0.0b	(.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1))
0.0b	(*.f64 (+.f64 a b) eps)
6.7b	(.f64 eps (.f64 1/2 (*.f64 a a)))
29.4b	(cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a))))
29.4b	(cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a))))
29.4b	(cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a))))

rewrite34.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
6×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow-prod-down_binary64_1172`
5×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
4×	`add-log-exp_binary64_1140`
3×	`pow1/3_binary64_1183` `associate-l_binary64_1042` `cbrt-prod_binary64_1132`
1×	`-commutative_binary64_1032` `associate-r*_binary64_1041`

Counts

4 → 48

Calls

8 calls:

8.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))
6.0ms	(cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a))))
6.0ms	(cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a))))
6.0ms	(cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a))))
0.0ms	(*.f64 (+.f64 a b) eps)

series862.0ms (0.7%)

Counts

4 → 24

Calls

4 calls:

262.0ms	(cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a))))
260.0ms	(cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a))))
257.0ms	(cbrt.f64 (.f64 eps (.f64 1/2 (*.f64 a a))))
82.0ms	(.f64 eps (.f64 1/2 (*.f64 a a)))

Compiler

Compiled 2628 to 1956 computations (25.6% saved)

simplify141.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4861	908
1	4861	908

localize40.0ms (0%)

Local error

Found 8 expressions with local error:

0.0b	(*.f64 eps (+.f64 b a))
0.0b	(+.f64 (exp.f64 (*.f64 a eps)) 1)
0.0b	(.f64 1/2 (.f64 eps eps))
0.0b	(+.f64 eps (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3))))))
3.7b	(+.f64 (exp.f64 (*.f64 eps (+.f64 b a))) -1)
3.8b	(/.f64 (.f64 (/.f64 eps (/.f64 (.f64 b (+.f64 eps (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))))) (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 a) eps))))) (+.f64 (exp.f64 (.f64 eps (+.f64 b a))) -1)) (/.f64 (+.f64 -1 (pow.f64 (exp.f64 a) (.f64 2 eps))) (sqrt.f64 (+.f64 (exp.f64 (.f64 a eps)) 1))))
7.8b	(.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))
11.2b	(/.f64 eps (/.f64 (.f64 b (+.f64 eps (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))))) (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 a) eps)))))

rewrite122.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

157×	`times-frac_binary64_1107`
118×	`*-un-lft-identity_binary64_1101`
67×	`add-sqr-sqrt_binary64_1123`
64×	`add-cube-cbrt_binary64_1136`
60×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
48×	`sqrt-prod_binary64_1117`
47×	`associate-/r*_binary64_1045`
30×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
27×	`distribute-lft-out_binary64_1052`
14×	`associate-/r/_binary64_1047`
12×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sqrt-div_binary64_1118`
10×	`flip3-+_binary64_1104` `flip-+_binary64_1075`
8×	`div-inv_binary64_1098`
6×	`add-log-exp_binary64_1140` `pow1_binary64_1162`
5×	`associate-/l/_binary64_1048`
4×	`associate-r/_binary64_1043` `associate-/l_binary64_1046`
3×	`associate-r_binary64_1041` `associate-l_binary64_1042`
2×	`frac-times_binary64_1111` `frac-2neg_binary64_1112` `clear-num_binary64_1100`
1×	`-commutative_binary64_1032` `sum-log_binary64_1192` `distribute-lft-in_binary64_1050` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `associate-l/_binary64_1044` `difference-of-sqr--1_binary64_1072` `distribute-rgt-in_binary64_1051`

Counts

4 → 212

Calls

8 calls:

41.0ms	(/.f64 (.f64 (/.f64 eps (/.f64 (.f64 b (+.f64 eps (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))))) (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 a) eps))))) (+.f64 (exp.f64 (.f64 eps (+.f64 b a))) -1)) (/.f64 (+.f64 -1 (pow.f64 (exp.f64 a) (.f64 2 eps))) (sqrt.f64 (+.f64 (exp.f64 (.f64 a eps)) 1))))
15.0ms	(/.f64 eps (/.f64 (.f64 b (+.f64 eps (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))))) (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 a) eps)))))
11.0ms	(.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))
5.0ms	(+.f64 (exp.f64 (*.f64 eps (+.f64 b a))) -1)
0.0ms	(+.f64 eps (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3))))))

series3.9s (3%)

Counts

4 → 40

Calls

4 calls:

3.2s	(/.f64 (.f64 (/.f64 eps (/.f64 (.f64 b (+.f64 eps (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))))) (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 a) eps))))) (+.f64 (exp.f64 (.f64 eps (+.f64 b a))) -1)) (/.f64 (+.f64 -1 (pow.f64 (exp.f64 a) (.f64 2 eps))) (sqrt.f64 (+.f64 (exp.f64 (.f64 a eps)) 1))))
415.0ms	(/.f64 eps (/.f64 (.f64 b (+.f64 eps (.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (.f64 1/6 (pow.f64 eps 3))))))) (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 a) eps)))))
119.0ms	(.f64 b (+.f64 (.f64 1/2 (.f64 eps eps)) (.f64 b (*.f64 1/6 (pow.f64 eps 3)))))
91.0ms	(+.f64 (exp.f64 (*.f64 eps (+.f64 b a))) -1)

Compiler

Compiled 7287 to 5028 computations (31% saved)

simplify182.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4987	16337
1	4987	16337

prune29.5s (22.6%)

Pruning

631 alts after pruning (620 fresh and 11 done)

	Pruned	Kept	Total
New	318	174	492
Fresh	12	446	458
Picked	0	0	0
Done	0	11	11
Total	330	631	961

Error

Counts

961 → 631

Compiler

Compiled 16092 to 8498 computations (47.2% saved)

simplify1.1s (0.9%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5114	74204

regimes10.0s (7.7%)

Compiler: Compiled 117378 to 79293 computations (32.4% saved)

bsearch0.0ms (0%)

regimes74.0ms (0.1%)

Compiler: Compiled 75 to 120 computations (-60% saved)

bsearch213.0ms (0.2%)

Steps

Iters

Range

Point

2.2536164736944188e-128

4.241974850863826e-126

2.2873523470155514e-128

-3.503872912532929e-97

-1.0564948238594488e-101

-1.0774485526151028e-101

-1.5799914207351828e+175

-6.522482963306561e+171

-2.9368846088630596e+173

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes98.0ms (0.1%)

Compiler: Compiled 33 to 84 computations (-154.5% saved)

bsearch141.0ms (0.1%)

Steps

Iters	Range		Point
8	2.8234002134000204e+45	1.1026497555246465e+48	2.8471803732139122e+45
9	-1.13753150809824e+16	-27152218162.99716	-29973173135.65804

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes29.0ms (0%)

Compiler: Compiled 24 to 69 computations (-187.5% saved)

bsearch0.0ms (0%)

regimes25.0ms (0%)

Accuracy

Total 3.1b remaining (99.5%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch4.0ms (0%)

Compiler: Compiled 61 to 55 computations (9.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	76
1	36	76

end0.0ms (0%)

sample35.9s (27.6%)

Algorithm

1×

intervals

Results

3.0s	4059×	body	2048	valid
948.0ms	2496×	body	1024	valid
221.0ms	9663×	pre	128	true
204.0ms	419×	body	2048	overflowed
168.0ms	543×	body	1024	overflowed
157.0ms	693×	body	512	valid
57.0ms	275×	body	512	overflowed
40.0ms	256×	body	256	valid
33.0ms	486×	body	128	valid
20.0ms	139×	body	256	overflowed
19.0ms	284×	body	128	overflowed
13.0ms	10×	body	4096	valid
2.0ms	3×	body	2048	invalid

Compiler

Compiled 39321 to 26623 computations (32.3% saved)

Pareto

0.4576317037312967