Details

analyze1.5s (9%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	75%	25%	3
0%	62.5%	37.5%	4
0%	56.2%	43.8%	5
3.1%	46.9%	50%	6
3.1%	45.3%	51.6%	7
3.1%	44.5%	52.4%	8
3.5%	44.1%	52.4%	9
3.7%	43.9%	52.4%	10
3.8%	43.8%	52.4%	11
3.8%	43.8%	52.4%	12
3.8%	43.8%	52.4%	13
3.8%	43.7%	52.4%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample384.0ms (2.3%)

Algorithm

1×

intervals

Results

117.0ms	132×	body	1024	valid
107.0ms	138×	body	1024	nan
40.0ms	71×	body	512	nan
34.0ms	55×	body	512	valid
21.0ms	13×	body	2048	valid
15.0ms	33×	body	256	valid
14.0ms	38×	body	256	nan
5.0ms	23×	body	128	valid

Compiler

Compiled 75 to 62 computations (17.3% saved)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4795	55
1	4795	55

prune14.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

60.9b

Counts

2 → 1

Compiler

Compiled 64 to 48 computations (25% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (/.f64 PI.f64 4) f)
0.2b	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
0.8b	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
6.1b	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))

rewrite538.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

60.8b

Rules

94×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
34×	`log-prod_binary64`
30×	`difference-of-squares_binary64`
15×	`distribute-lft-out_binary64`
14×	`add-exp-log_binary64`
13×	`unpow-prod-down_binary64` `associate-l_binary64`
11×	`add-cbrt-cube_binary64` `sqr-pow_binary64`
10×	`distribute-lft-out--_binary64`
7×	`pow1_binary64` `cancel-sign-sub-inv_binary64` `associate-/r*_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `associate-/l*_binary64`
3×	`flip3--_binary64` `flip--_binary64` `div-exp_binary64` `div-inv_binary64` `associate-r_binary64`
2×	`cbrt-undiv_binary64` `associate-/l/_binary64` `rem-log-exp_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `frac-2neg_binary64` `clear-num_binary64` `flip3-+_binary64` `flip-+_binary64` `log-pow_binary64` `log-div_binary64` `pow-prod-down_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 154

Calls

4 calls:

13.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
13.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
8.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
7.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 6588 to 4435 computations (32.7% saved)

series901.0ms (5.4%)

Error

1.9b

Counts

4 → 12

Calls

4 calls:

543.0ms	(log.f64 (/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))))
218.0ms	(/.f64 (+.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))) (-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f))))
74.0ms	(-.f64 (exp.f64 (.f64 (/.f64 PI.f64 4) f)) (pow.f64 (exp.f64 -1/4) (.f64 PI.f64 f)))
47.0ms	(*.f64 (/.f64 PI.f64 4) f)

Compiler

Compiled 1227 to 952 computations (22.4% saved)

simplify121.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5005	8522

prune395.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	158	8	166
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	8	167

Error

1.9b

Counts

167 → 8

Compiler

Compiled 6191 to 4211 computations (32% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(-.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 1/2))) (log.f64 f))
0.4b	(.f64 (-.f64 (log.f64 (/.f64 2 (.f64 PI.f64 1/2))) (log.f64 f)) (/.f64 -4 PI.f64))
2.0b	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))

rewrite163.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

26×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
17×	`add-cube-cbrt_binary64` `log-prod_binary64`
16×	`times-frac_binary64`
15×	`pow1_binary64`
14×	`add-exp-log_binary64`
13×	`associate-r_binary64`
10×	`log-pow_binary64`
8×	`add-cbrt-cube_binary64` `associate-l_binary64` `distribute-lft-out--_binary64`
7×	`associate--l+_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`div-inv_binary64` `prod-exp_binary64` `div-exp_binary64` `rem-log-exp_binary64` `add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `associate--r+_binary64`
2×	`log-div_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `unswap-sqr_binary64` `associate-*l/_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `-commutative_binary64` `diff-log_binary64` `sub-neg_binary64` `associate--l-_binary64`

Counts

3 → 91

Calls

3 calls:

12.0ms	(.f64 (-.f64 (log.f64 (/.f64 2 (.f64 PI.f64 1/2))) (log.f64 f)) (/.f64 -4 PI.f64))
8.0ms	(-.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 1/2))) (log.f64 f))
4.0ms	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))

Compiler

Compiled 1771 to 1280 computations (27.7% saved)

series425.0ms (2.6%)

Error

1.7b

Counts

3 → 6

Calls

3 calls:

240.0ms	(.f64 (-.f64 (log.f64 (/.f64 2 (.f64 PI.f64 1/2))) (log.f64 f)) (/.f64 -4 PI.f64))
176.0ms	(-.f64 (log.f64 (/.f64 2 (*.f64 PI.f64 1/2))) (log.f64 f))
0.0ms	(log.f64 (/.f64 2 (*.f64 PI.f64 1/2)))

Compiler

Compiled 240 to 211 computations (12.1% saved)

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4959	1739
1	4959	1739

prune148.0ms (0.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	86	11	97
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	88	17	105

Error

1.5b

Counts

105 → 17

Compiler

Compiled 1939 to 1393 computations (28.2% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))
0.3b	(/.f64 (*.f64 -4 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))) PI.f64)
2.0b	(log.f64 (/.f64 4 PI.f64))

rewrite132.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

29×	`log-prod_binary64`
25×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`associate--l+_binary64`
11×	`add-exp-log_binary64`
9×	`pow1_binary64`
8×	`add-cbrt-cube_binary64`
6×	`log-pow_binary64`
4×	`cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64`
3×	`div-inv_binary64` `div-exp_binary64` `add-log-exp_binary64` `associate-/r*_binary64` `associate--r+_binary64`
2×	`log-div_binary64` `rem-log-exp_binary64` `cbrt-undiv_binary64` `flip3--_binary64` `associate-*r/_binary64` `associate-/l/_binary64` `flip--_binary64`
1×	`prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l*_binary64` `diff-log_binary64` `sub-neg_binary64` `difference-of-squares_binary64` `associate--l-_binary64`

Counts

3 → 84

Calls

3 calls:

12.0ms	(/.f64 (*.f64 -4 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))) PI.f64)
7.0ms	(-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))
3.0ms	(log.f64 (/.f64 4 PI.f64))

Compiler

Compiled 1464 to 972 computations (33.6% saved)

series408.0ms (2.5%)

Error

1.5b

Counts

3 → 6

Calls

3 calls:

240.0ms	(/.f64 (*.f64 -4 (-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))) PI.f64)
162.0ms	(-.f64 (log.f64 (/.f64 4 PI.f64)) (log.f64 f))
0.0ms	(log.f64 (/.f64 4 PI.f64))

Compiler

Compiled 240 to 211 computations (12.1% saved)

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	6082	1449

prune118.0ms (0.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	3	13	16
Picked	1	0	1
Done	0	0	0
Total	91	16	107

Error

1.5b

Counts

107 → 16

Compiler

Compiled 1669 to 1170 computations (29.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(log.f64 (/.f64 (sqrt.f64 4) (sqrt.f64 PI.f64)))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(log.f64 (/.f64 2 (sqrt.f64 PI.f64)))

rewrite169.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

1.5b

Rules

62×	`log-prod_binary64`
54×	`times-frac_binary64`
51×	`sqrt-prod_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
10×	`add-exp-log_binary64`
8×	`pow1_binary64`
4×	`rem-log-exp_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
2×	`log-pow_binary64` `log-div_binary64` `div-inv_binary64` `div-exp_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 110

Calls

4 calls:

6.0ms	(log.f64 (/.f64 (sqrt.f64 4) (sqrt.f64 PI.f64)))
4.0ms	(log.f64 (/.f64 2 (sqrt.f64 PI.f64)))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 2391 to 1540 computations (35.6% saved)

series1.0ms (0%)

Error

1.5b

Counts

4 → 0

Calls

4 calls:

0.0ms	(log.f64 (/.f64 2 (sqrt.f64 PI.f64)))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(log.f64 (/.f64 (sqrt.f64 4) (sqrt.f64 PI.f64)))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 0 to 0 computations (0% saved)

simplify101.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4809	1747
1	4809	1747

prune117.0ms (0.7%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	110	16	126

Error

1.5b

Counts

126 → 16

Compiler

Compiled 1777 to 1127 computations (36.6% saved)

regimes1.6s (9.4%)

Accuracy

Total 2.3b remaining (85.1%)

Threshold costs 0b (0%)

Compiler

Compiled 19920 to 15494 computations (22.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	19
1	24	19

end2.0ms (0%)

Compiler: Compiled 11 to 10 computations (9.1% saved)

sample9.2s (55.1%)

Algorithm

1×

intervals

Results

2.6s	3878×	body	1024	valid
2.4s	3852×	body	1024	nan
940.0ms	1983×	body	512	valid
876.0ms	1981×	body	512	nan
676.0ms	495×	body	2048	valid
305.0ms	951×	body	256	valid
286.0ms	971×	body	256	nan
113.0ms	693×	body	128	valid
5.0ms	4×	body	2048	nan
0.0ms	2×	body	128	nan
0.0ms	1×	body	128	overflowed

Compiler

Compiled 534 to 425 computations (20.4% saved)

Details

analyze1.5s (9%)

sample384.0ms (2.3%)

simplify80.0ms (0.5%)

prune14.0ms (0.1%)

localize20.0ms (0.1%)

rewrite538.0ms (3.2%)

series901.0ms (5.4%)

simplify121.0ms (0.7%)

prune395.0ms (2.4%)

localize11.0ms (0.1%)

rewrite163.0ms (1%)

series425.0ms (2.6%)

simplify79.0ms (0.5%)

prune148.0ms (0.9%)

localize9.0ms (0.1%)

rewrite132.0ms (0.8%)

series408.0ms (2.5%)

simplify60.0ms (0.4%)

prune118.0ms (0.7%)

localize17.0ms (0.1%)

rewrite169.0ms (1%)

series1.0ms (0%)

simplify101.0ms (0.6%)

prune117.0ms (0.7%)

regimes1.6s (9.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end2.0ms (0%)

sample9.2s (55.1%)

Profiling