Details

analyze1.7s (9.3%)

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)

sample200.0ms (1.1%)

Algorithm

1×

intervals

Results

116.0ms	129×	body	2048	valid
34.0ms	79×	body	1024	valid
10.0ms	24×	body	1024	overflowed
8.0ms	18×	body	2048	overflowed
7.0ms	323×	pre	128	true
4.0ms	17×	body	512	valid
2.0ms	8×	body	512	overflowed
2.0ms	22×	body	128	valid
1.0ms	8×	body	256	valid
1.0ms	15×	body	128	overflowed
1.0ms	1×	body	4096	valid
0.0ms	2×	body	256	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify186.0ms (1%)

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: 59.1b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
3.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
3.9b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
6.3b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1133`
26×	`*-un-lft-identity_binary64_1111`
15×	`cancel-sign-sub-inv_binary64_1077`
11×	`add-cube-cbrt_binary64_1146`
10×	`difference-of-squares_binary64_1080` `add-log-exp_binary64_1150`
9×	`flip3--_binary64_1115` `flip--_binary64_1086`
7×	`associate-r_binary64_1051` `associate-l_binary64_1052`
6×	`add-cbrt-cube_binary64_1147` `pow1_binary64_1172` `add-exp-log_binary64_1149`
5×	`difference-of-sqr-1_binary64_1081` `sub-neg_binary64_1104` `distribute-lft-out--_binary64_1063`
4×	`frac-times_binary64_1121` `distribute-lft-in_binary64_1060` `distribute-rgt-in_binary64_1061`
3×	`diff-log_binary64_1203`
2×	`associate-l/_binary64_1054` `associate-r/_binary64_1053`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `pow-prod-down_binary64_1182` `unswap-sqr_binary64_1079`

Counts

4 → 96

Calls

4 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)

series256.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
74.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
47.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)
44.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)

simplify73.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4986	2058
1	4986	2058

prune242.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	4	109

Merged error: 50.8b

Counts

109 → 4

Compiler

Compiled 5571 to 2923 computations (47.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.5b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.0b	(/.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)))))))
6.3b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
12.1b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite56.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
16×	`add-sqr-sqrt_binary64_1133`
13×	`*-un-lft-identity_binary64_1111`
9×	`pow1_binary64_1172`
8×	`add-log-exp_binary64_1150` `associate-/r/_binary64_1057`
7×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `add-cube-cbrt_binary64_1146`
6×	`cancel-sign-sub-inv_binary64_1077` `flip3--_binary64_1115` `flip--_binary64_1086` `associate-*r/_binary64_1053`
4×	`flip-+_binary64_1085` `frac-times_binary64_1121` `flip3-+_binary64_1114` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `difference-of-squares_binary64_1080`
3×	`associate-r_binary64_1051` `pow-prod-down_binary64_1182`
2×	`associate-*l/_binary64_1054` `associate-/l/_binary64_1058` `diff-log_binary64_1203` `difference-of-sqr-1_binary64_1081` `sub-neg_binary64_1104` `distribute-lft-out--_binary64_1063`
1×	`-commutative_binary64_1042` `times-frac_binary64_1117` `div-inv_binary64_1108` `associate-/r_binary64_1055` `distribute-lft-in_binary64_1060` `frac-2neg_binary64_1122` `associate-/l_binary64_1056` `associate-l*_binary64_1052` `unswap-sqr_binary64_1079` `distribute-rgt-in_binary64_1061` `clear-num_binary64_1110`

Counts

4 → 90

Calls

4 calls:

18.0ms	(/.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)))))))
13.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series8.3s (46.2%)

Counts

4 → 12

Calls

4 calls:

8.0s	(/.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)))))))
176.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
84.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
43.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify89.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4960	3717
1	4960	3717

prune402.0ms (2.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	102	4	106

Merged error: 0.1b

Counts

106 → 4

Compiler

Compiled 9502 to 5536 computations (41.7% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1111`
7×	`distribute-lft-out_binary64_1062`
6×	`times-frac_binary64_1117`
4×	`div-inv_binary64_1108`
3×	`add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146` `add-log-exp_binary64_1150`
1×	`add-cbrt-cube_binary64_1147` `flip-+_binary64_1085` `flip3-+_binary64_1114` `+-commutative_binary64_1041` `frac-add_binary64_1119` `pow1_binary64_1172` `sum-log_binary64_1202` `add-exp-log_binary64_1149`

Counts

1 → 19

Calls

1 calls:

18.0ms

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

series20.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

19.0ms

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

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4970	287
1	4970	287

prune62.0ms (0.3%)

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 1110 to 874 computations (21.3% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

15.1b

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

rewrite9.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64_1111`
6×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
4×	`times-frac_binary64_1117` `associate-/l*_binary64_1056`
3×	`add-sqr-sqrt_binary64_1133` `add-cube-cbrt_binary64_1146`
2×	`associate-/l/_binary64_1058` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `distribute-lft-out_binary64_1062`
1×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `flip-+_binary64_1085` `associate-/r*_binary64_1055` `frac-2neg_binary64_1122` `flip3-+_binary64_1114` `add-log-exp_binary64_1150` `pow1_binary64_1172` `clear-num_binary64_1110`

Counts

1 → 25

Calls

1 calls:

7.0ms

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

series61.0ms (0.3%)

Counts

1 → 3

Calls

1 calls:

61.0ms

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

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5129	354

prune56.0ms (0.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	27	1	28
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	28	7	35

Merged error: 0.0b

Counts

35 → 7

Compiler

Compiled 1014 to 648 computations (36.1% saved)

regimes56.0ms (0.3%)

Compiler: Compiled 462 to 381 computations (17.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	9	10

end0.0ms (0%)

sample6.0s (33.3%)

Algorithm

1×

intervals

Results

3.4s	4099×	body	2048	valid
1.0s	2377×	body	1024	valid
230.0ms	9704×	pre	128	true
206.0ms	396×	body	2048	overflowed
188.0ms	747×	body	512	valid
184.0ms	558×	body	1024	overflowed
61.0ms	292×	body	512	overflowed
39.0ms	252×	body	256	valid
38.0ms	512×	body	128	valid
23.0ms	172×	body	256	overflowed
20.0ms	282×	body	128	overflowed
18.0ms	13×	body	4096	valid
5.0ms	4×	body	2048	invalid

Compiler

Compiled 197 to 162 computations (17.8% saved)

Details

analyze1.7s (9.3%)

sample200.0ms (1.1%)

simplify186.0ms (1%)

prune3.0ms (0%)

localize20.0ms (0.1%)

rewrite39.0ms (0.2%)

series256.0ms (1.4%)

simplify73.0ms (0.4%)

prune242.0ms (1.3%)

localize25.0ms (0.1%)

rewrite56.0ms (0.3%)

series8.3s (46.2%)

simplify89.0ms (0.5%)

prune402.0ms (2.2%)

localize5.0ms (0%)

rewrite19.0ms (0.1%)

series20.0ms (0.1%)

simplify60.0ms (0.3%)

prune62.0ms (0.3%)

localize4.0ms (0%)

rewrite9.0ms (0%)

series61.0ms (0.3%)

simplify67.0ms (0.4%)

prune56.0ms (0.3%)

regimes56.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.0s (33.3%)

Profiling