Details

analyze1.1s (5.5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5644	164
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample61.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	166×	body	128	valid
12.0ms	42×	body	1024	valid
7.0ms	32×	body	512	valid
6.0ms	23×	body	1024	nan
3.0ms	46×	body	128	nan
2.0ms	12×	body	512	nan
2.0ms	16×	body	256	valid
1.0ms	9×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5192	41

prune3.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

43.3b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.5b	(*.f64 (sqrt.f64 2) t)
12.8b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
19.9b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite233.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

43.1b

Rules

17×	`add-sqr-sqrt_binary64_100`
13×	`sqrt-prod_binary64_94`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
7×	`pow1_binary64_139`
6×	`add-log-exp_binary64_117` `associate-l_binary64_19` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `associate-r_binary64_18`
2×	`associate--l+_binary64_15` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `sub-neg_binary64_71` `cancel-sign-sub-inv_binary64_44` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `pow-prod-down_binary64_149` `-commutative_binary64_9` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23`

Counts

4 → 80

Calls

4 calls:

19.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
19.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
15.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
5.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3564 to 2030 computations (43% saved)

series5.0s (25.5%)

Error

5.5b

Counts

4 → 57

Calls

4 calls:

3.4s	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
745.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
699.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
32.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 10298 to 8546 computations (17% saved)

simplify89.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5136	6022

prune272.0ms (1.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	130	8	138

Error

5.5b

Counts

138 → 8

Compiler

Compiled 5800 to 3573 computations (38.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.3b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
6.9b	(/.f64 (*.f64 l l) x)
10.4b	(/.f64 (*.f64 t t) x)
26.1b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite163.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

14×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
10×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`sqrt-div_binary64_95` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `sqrt-prod_binary64_94`
2×	`associate-r/_binary64_20` `frac-add_binary64_86` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `sum-log_binary64_169` `+-commutative_binary64_8`

Counts

4 → 70

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
7.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.0ms	(/.f64 (*.f64 t t) x)
4.0ms	(/.f64 (*.f64 l l) x)

Compiler

Compiled 2731 to 1340 computations (50.9% saved)

series839.0ms (4.3%)

Error

0.6b

Counts

4 → 43

Calls

4 calls:

484.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
143.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
74.0ms	(/.f64 (*.f64 l l) x)
72.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 4155 to 3358 computations (19.2% saved)

simplify72.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5037	2638

prune175.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	106	7	113
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	109	12	121

Error

0.5b

Counts

121 → 12

Compiler

Compiled 3970 to 2215 computations (44.2% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (sqrt.f64 2) t)
3.3b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
10.4b	(/.f64 (*.f64 t t) x)
26.1b	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite138.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

15×	`add-sqr-sqrt_binary64_100`
11×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
10×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`pow1_binary64_139` `sqrt-prod_binary64_94`
6×	`add-log-exp_binary64_117` `associate-l_binary64_19`
4×	`associate-*r/_binary64_20` `sqrt-div_binary64_95`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `times-frac_binary64_84` `associate-/r_binary64_22` `associate-r*_binary64_18`
2×	`frac-add_binary64_86` `prod-exp_binary64_127` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23` `sum-log_binary64_169` `+-commutative_binary64_8` `pow-prod-down_binary64_149` `-commutative_binary64_9`

Counts

4 → 71

Calls

4 calls:

13.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
7.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.0ms	(*.f64 (sqrt.f64 2) t)
5.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 2767 to 1393 computations (49.7% saved)

series781.0ms (4%)

Error

0.5b

Counts

4 → 40

Calls

4 calls:

486.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
133.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
73.0ms	(/.f64 (*.f64 t t) x)
30.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3912 to 3169 computations (19% saved)

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4967	2608
1	4967	2608

prune172.0ms (0.9%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	109	14	123

Error

0.5b

Counts

123 → 14

Compiler

Compiled 3991 to 2271 computations (43.1% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x))))
3.3b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
10.4b	(/.f64 (*.f64 t t) x)
26.1b	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite159.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

11×	`add-log-exp_binary64_117`
9×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
8×	`add-sqr-sqrt_binary64_100` `associate-*r/_binary64_20`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139` `flip3-+_binary64_81` `flip-+_binary64_52`
4×	`frac-add_binary64_86` `sqrt-div_binary64_95` `sum-log_binary64_169`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `+-commutative_binary64_8`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l*_binary64_23` `associate-+r+_binary64_10`

Counts

4 → 64

Calls

4 calls:

13.0ms	(+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x))))
13.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
7.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 3159 to 1703 computations (46.1% saved)

series1.2s (6%)

Error

0.5b

Counts

4 → 55

Calls

4 calls:

501.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
374.0ms	(+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x))))
149.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
76.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 5364 to 4569 computations (14.8% saved)

simplify98.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4957	3448
1	4957	3448

prune198.0ms (1%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	116	3	119
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	116	17	133

Error

0.5b

Counts

133 → 17

Compiler

Compiled 4466 to 2653 computations (40.6% saved)

regimes2.8s (14.1%)

Accuracy

Total 8.7b remaining (95.4%)

Threshold costs 0b (0%)

Compiler

Compiled 34054 to 25033 computations (26.5% saved)

bsearch620.0ms (3.1%)

Steps

Iters	Range		Point
6	4.277011105369588e+69	4.91400541908726e+70	3.6158306802905055e+70
10	1.068100816811621e-126	1.8774915301848425e-113	1.0839695737903189e-126
7	1.0530080621813793e-225	6.8489574660780605e-224	6.747218417347291e-224
10	-4.637117794060303e-217	-1.7094100243374133e-231	-4.552217556014532e-217
9	-1.6621105471744934e-169	-7.80041967121216e-177	-7.8940362468376395e-177
7	-4.2337420537778665e+93	-1.6554168458226126e+91	-3.094785260795066e+93

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	144	290
1	144	290

end0.0ms (0%)

sample5.3s (27.1%)

Algorithm

1×

intervals

Results

398.0ms	5329×	body	128	valid
326.0ms	1172×	body	1024	valid
233.0ms	837×	body	1024	nan
192.0ms	908×	body	512	valid
109.0ms	1536×	body	128	nan
106.0ms	504×	body	512	nan
75.0ms	524×	body	256	valid
42.0ms	316×	body	256	nan
26.0ms	67×	body	2048	valid

Compiler

Compiled 5054 to 3733 computations (26.1% saved)

Details

analyze1.1s (5.5%)

sample61.0ms (0.3%)

simplify72.0ms (0.4%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite233.0ms (1.2%)

series5.0s (25.5%)

simplify89.0ms (0.4%)

prune272.0ms (1.4%)

localize21.0ms (0.1%)

rewrite163.0ms (0.8%)

series839.0ms (4.3%)

simplify72.0ms (0.4%)

prune175.0ms (0.9%)

localize21.0ms (0.1%)

rewrite138.0ms (0.7%)

series781.0ms (4%)

simplify74.0ms (0.4%)

prune172.0ms (0.9%)

localize20.0ms (0.1%)

rewrite159.0ms (0.8%)

series1.2s (6%)

simplify98.0ms (0.5%)

prune198.0ms (1%)

regimes2.8s (14.1%)

bsearch620.0ms (3.1%)

simplify5.0ms (0%)

end0.0ms (0%)

sample5.3s (27.1%)

Profiling