Details

analyze1.7s (11.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5719	148
0	3	3
1	3	3

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)

sample177.0ms (1.2%)

Algorithm

1×

intervals

Results

104.0ms	137×	body	2048	valid
26.0ms	71×	body	1024	valid
7.0ms	303×	pre	128	true
6.0ms	19×	body	1024	overflowed
4.0ms	20×	body	512	valid
3.0ms	6×	body	2048	overflowed
2.0ms	8×	body	512	overflowed
1.0ms	19×	body	128	valid
1.0ms	9×	body	256	valid
1.0ms	5×	body	256	overflowed
1.0ms	9×	body	128	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5217	37

prune6.0ms (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: 60.0b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize16.0ms (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))
1.8b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
2.8b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.4b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite35.0ms (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)
4.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
4.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series149.0ms (1%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
42.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
30.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
27.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify90.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4967	2058
1	4967	2058

prune147.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Merged error: 49.2b

Counts

109 → 3

Compiler

Compiled 3422 to 1407 computations (58.9% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
3.4b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
3.8b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.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)))))))
12.4b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite52.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_1139`
26×	`add-cbrt-cube_binary64_1137`
14×	`prod-exp_binary64_1150`
12×	`add-sqr-sqrt_binary64_1123`
11×	`pow1_binary64_1162`
10×	`cbrt-unprod_binary64_1134` `*-un-lft-identity_binary64_1101`
8×	`associate-/r/_binary64_1047`
7×	`add-cube-cbrt_binary64_1136`
6×	`add-log-exp_binary64_1140` `associate-*r/_binary64_1043`
5×	`flip--_binary64_1076` `flip3--_binary64_1105`
4×	`frac-times_binary64_1111` `flip3-+_binary64_1104` `associate-r_binary64_1041` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `associate-l_binary64_1042`
3×	`cancel-sign-sub-inv_binary64_1067`
2×	`-commutative_binary64_1032` `difference-of-squares_binary64_1070` `associate-/l/_binary64_1048` `associate-l/_binary64_1044`
1×	`diff-log_binary64_1193` `pow-exp_binary64_1169` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `difference-of-sqr-1_binary64_1071` `distribute-lft-in_binary64_1050` `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` `pow-to-exp_binary64_1170` `distribute-rgt-in_binary64_1051` `associate-/r_binary64_1045`

Counts

4 → 91

Calls

4 calls:

17.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.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)))))))
12.0ms	(.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)

series4.6s (31%)

Counts

4 → 12

Calls

4 calls:

4.4s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.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)))))))
99.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
43.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
42.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5017	3682

prune219.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	102	4	106

Merged error: 0.0b

Counts

106 → 4

Compiler

Compiled 5287 to 2594 computations (50.9% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite15.0ms (0.1%)

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

1 calls:

13.0ms

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

series10.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

10.0ms

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

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4871	287
1	4871	287

prune26.0ms (0.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	19	7	26

Merged error: 0.0b

Counts

26 → 7

Compiler

Compiled 418 to 321 computations (23.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

rewrite102.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64_1101`
114×	`cbrt-prod_binary64_1132`
81×	`distribute-lft-out_binary64_1052`
60×	`div-inv_binary64_1098`
42×	`times-frac_binary64_1107`
37×	`add-sqr-sqrt_binary64_1123`
33×	`swap-sqr_binary64_1068` `cbrt-div_binary64_1133`
29×	`add-cube-cbrt_binary64_1136`
13×	`associate-r_binary64_1041` `associate-l_binary64_1042`
11×	`pow1_binary64_1162` `flip3-+_binary64_1104` `flip-+_binary64_1075` `frac-add_binary64_1109`
9×	`pow1/3_binary64_1183` `frac-times_binary64_1111`
6×	`add-exp-log_binary64_1139`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137` `unswap-sqr_binary64_1069`
3×	`associate-r/_binary64_1043` `associate-l/_binary64_1044`
2×	`pow-prod-up_binary64_1171` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow2_binary64_1182`

Counts

4 → 159

Calls

4 calls:

41.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
13.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series342.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

106.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
83.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
80.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
73.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify87.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4942	3863
1	4942	3863

prune322.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	171	7	178

Merged error: 0.0b

Counts

178 → 7

Compiler

Compiled 5309 to 4131 computations (22.2% saved)

regimes328.0ms (2.2%)

Compiler: Compiled 4734 to 3416 computations (27.8% 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	51	137
1	51	137

end0.0ms (0%)

sample6.1s (41.4%)

Algorithm

1×

intervals

Results

3.0s	4152×	body	2048	valid
848.0ms	2283×	body	1024	valid
222.0ms	9794×	pre	128	true
198.0ms	652×	body	1024	overflowed
171.0ms	367×	body	2048	overflowed
169.0ms	756×	body	512	valid
64.0ms	327×	body	512	overflowed
37.0ms	267×	body	256	valid
37.0ms	532×	body	128	valid
21.0ms	163×	body	256	overflowed
19.0ms	283×	body	128	overflowed
11.0ms	10×	body	4096	valid
2.0ms	2×	body	2048	invalid

Compiler

Compiled 1296 to 924 computations (28.7% saved)

Details

analyze1.7s (11.6%)

sample177.0ms (1.2%)

simplify24.0ms (0.2%)

prune6.0ms (0%)

localize16.0ms (0.1%)

rewrite35.0ms (0.2%)

series149.0ms (1%)

simplify90.0ms (0.6%)

prune147.0ms (1%)

localize28.0ms (0.2%)

rewrite52.0ms (0.4%)

series4.6s (31%)

simplify68.0ms (0.5%)

prune219.0ms (1.5%)

localize8.0ms (0.1%)

rewrite15.0ms (0.1%)

series10.0ms (0.1%)

simplify87.0ms (0.6%)

prune26.0ms (0.2%)

localize12.0ms (0.1%)

rewrite102.0ms (0.7%)

series342.0ms (2.3%)

simplify87.0ms (0.6%)

prune322.0ms (2.2%)

regimes328.0ms (2.2%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.1s (41.4%)

Profiling