Details

analyze1.8s (11.8%)

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)

sample180.0ms (1.1%)

Algorithm

1×

intervals

Results

97.0ms	123×	body	2048	valid
33.0ms	78×	body	1024	valid
8.0ms	24×	body	1024	overflowed
7.0ms	312×	pre	128	true
7.0ms	12×	body	2048	overflowed
7.0ms	24×	body	512	valid
2.0ms	8×	body	512	overflowed
2.0ms	10×	body	256	valid
2.0ms	21×	body	128	valid
1.0ms	5×	body	256	overflowed
1.0ms	7×	body	128	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify113.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5217	37

prune3.0ms (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

Merged error: 59.2b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.2b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.7b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite34.0ms (0.2%)

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

4 calls:

12.0ms	(.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)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series147.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
43.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
26.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
24.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify89.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4967	2058
1	4967	2058

prune142.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Merged error: 48.2b

Counts

109 → 6

Compiler

Compiled 3521 to 1479 computations (58% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps))))))
3.3b	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
4.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
13.7b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite47.0ms (0.3%)

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

4 calls:

14.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
10.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps))))))
6.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series406.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps))))))
97.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
47.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
43.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5167	2978

prune209.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	6	104
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	100	10	110

Merged error: 47.6b

Counts

110 → 10

Compiler

Compiled 5368 to 2611 computations (51.4% saved)

localize27.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2))))))
4.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0b	(.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))
6.9b	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))

rewrite61.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

15.0ms	(.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))
14.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2))))))
13.0ms	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series394.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

208.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2))))))
72.0ms	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))
70.0ms	(.f64 b (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))
43.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4959	3564
1	4959	3564

prune213.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	125	9	134

Merged error: 47.6b

Counts

134 → 9

Compiler

Compiled 5948 to 2883 computations (51.5% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.2b	(+.f64 -1 (exp.f64 (*.f64 eps a)))
3.2b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 b (+.f64 -1 (exp.f64 (.f64 eps a)))) (+.f64 eps (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))))
4.0b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
6.9b	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))

rewrite53.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
15×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
14×	`associate-*r/_binary64_1043`
13×	`pow1_binary64_1162`
11×	`*-un-lft-identity_binary64_1101`
10×	`add-sqr-sqrt_binary64_1123`
8×	`add-log-exp_binary64_1140` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `flip-+_binary64_1075`
6×	`add-cube-cbrt_binary64_1136` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
4×	`frac-times_binary64_1111` `distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
3×	`associate-l_binary64_1042` `cancel-sign-sub-inv_binary64_1067`
2×	`difference-of-squares_binary64_1070` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/l/_binary64_1048` `associate-*l/_binary64_1044`
1×	`diff-log_binary64_1193` `-commutative_binary64_1032` `distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `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` `associate-r_binary64_1041` `+-commutative_binary64_1031` `associate-/r*_binary64_1045`

Counts

4 → 92

Calls

4 calls:

16.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 b (+.f64 -1 (exp.f64 (.f64 eps a)))) (+.f64 eps (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))))
13.0ms	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
3.0ms	(+.f64 -1 (exp.f64 (*.f64 eps a)))

series4.3s (27.2%)

Counts

4 → 12

Calls

4 calls:

4.1s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (.f64 b (+.f64 -1 (exp.f64 (.f64 eps a)))) (+.f64 eps (.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (.f64 b 1/6) eps) 1/2))))))
79.0ms	(.f64 b (.f64 (.f64 eps eps) (+.f64 (.f64 (*.f64 b 1/6) eps) 1/2)))
41.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
23.0ms	(+.f64 -1 (exp.f64 (*.f64 eps a)))

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5007	3666

prune179.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	108	5	113

Merged error: 0.1b

Counts

113 → 5

Compiler

Compiled 4727 to 2333 computations (50.6% saved)

regimes358.0ms (2.3%)

Compiler: Compiled 5858 to 4008 computations (31.6% saved)

bsearch3.0ms (0%)

Compiler: Compiled 24 to 19 computations (20.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	148
1	56	148

end0.0ms (0%)

sample6.6s (42%)

Algorithm

1×

intervals

Results

3.2s	4069×	body	2048	valid
1.0s	2417×	body	1024	valid
234.0ms	9693×	pre	128	true
208.0ms	599×	body	1024	overflowed
198.0ms	754×	body	512	valid
196.0ms	367×	body	2048	overflowed
69.0ms	291×	body	512	overflowed
41.0ms	514×	body	128	valid
38.0ms	233×	body	256	valid
25.0ms	153×	body	256	overflowed
22.0ms	282×	body	128	overflowed
14.0ms	13×	body	4096	valid
1.0ms	1×	body	2048	invalid

Compiler

Compiled 1584 to 1074 computations (32.2% saved)

Details

analyze1.8s (11.8%)

sample180.0ms (1.1%)

simplify113.0ms (0.7%)

prune3.0ms (0%)

localize21.0ms (0.1%)

rewrite34.0ms (0.2%)

series147.0ms (0.9%)

simplify89.0ms (0.6%)

prune142.0ms (0.9%)

localize28.0ms (0.2%)

rewrite47.0ms (0.3%)

series406.0ms (2.6%)

simplify83.0ms (0.5%)

prune209.0ms (1.3%)

localize27.0ms (0.2%)

rewrite61.0ms (0.4%)

series394.0ms (2.5%)

simplify101.0ms (0.6%)

prune213.0ms (1.4%)

localize26.0ms (0.2%)

rewrite53.0ms (0.3%)

series4.3s (27.2%)

simplify71.0ms (0.4%)

prune179.0ms (1.1%)

regimes358.0ms (2.3%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.6s (42%)

Profiling