Details

analyze1.3s (5.7%)

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)

sample62.0ms (0.3%)

Algorithm

1×

intervals

Results

15.0ms	171×	body	128	valid
10.0ms	31×	body	1024	valid
6.0ms	26×	body	512	valid
5.0ms	17×	body	1024	nan
4.0ms	25×	body	256	valid
3.0ms	38×	body	128	nan
2.0ms	10×	body	512	nan
1.0ms	3×	body	2048	valid
1.0ms	5×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify89.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

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

45.6b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize16.0ms (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))))
0.6b	(*.f64 (sqrt.f64 2) t)
14.1b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
22.8b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite283.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

45.4b

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:

30.0ms	(/.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))))
15.0ms	(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)

series6.4s (28%)

Error

8.4b

Counts

4 → 55

Calls

4 calls:

4.4s	(/.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))))
965.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
838.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
34.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 10306 to 8551 computations (17% saved)

simplify102.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5273	5918

prune336.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	127	8	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	8	136

Error

8.4b

Counts

136 → 8

Compiler

Compiled 5692 to 3568 computations (37.3% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.8b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.9b	(/.f64 (*.f64 l l) x)
9.9b	(/.f64 (*.f64 t t) x)
30.0b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite177.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

5.1b

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)))))
8.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
7.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 2731 to 1340 computations (50.9% saved)

series965.0ms (4.2%)

Error

0.4b

Counts

4 → 41

Calls

4 calls:

555.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
169.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
86.0ms	(/.f64 (*.f64 l l) x)
85.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 3983 to 3208 computations (19.5% saved)

simplify101.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4991	2491
1	4991	2491

prune205.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	108	11	119

Error

0.4b

Counts

119 → 11

Compiler

Compiled 3814 to 2129 computations (44.2% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(*.f64 (sqrt.f64 2) t)
2.8b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
9.9b	(/.f64 (*.f64 t t) x)
30.0b	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite177.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

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:

27.0ms	(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)

series882.0ms (3.9%)

Error

0.4b

Counts

4 → 38

Calls

4 calls:

526.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
159.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
72.0ms	(/.f64 (*.f64 t t) x)
45.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3740 to 3019 computations (19.3% saved)

simplify83.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4969	2476
1	4969	2476

prune182.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	108	12	120

Error

0.4b

Counts

120 → 12

Compiler

Compiled 3800 to 2139 computations (43.7% saved)

localize30.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 t (sqrt.f64 (sqrt.f64 2))))
2.8b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
9.9b	(/.f64 (*.f64 t t) x)
30.0b	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite235.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

14×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
12×	`sqrt-prod_binary64_94`
11×	`add-sqr-sqrt_binary64_100`
10×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`associate-l_binary64_19`
6×	`add-log-exp_binary64_117`
4×	`associate-*r/_binary64_20` `sqrt-div_binary64_95` `prod-exp_binary64_127` `cbrt-unprod_binary64_111`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `times-frac_binary64_84` `associate-/r*_binary64_22` `pow-prod-down_binary64_149`
2×	`frac-add_binary64_86` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
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` `associate-r_binary64_18` `-commutative_binary64_9`

Counts

4 → 73

Calls

4 calls:

19.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
15.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 t (sqrt.f64 (sqrt.f64 2))))
7.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 3242 to 1850 computations (42.9% saved)

series974.0ms (4.3%)

Error

0.4b

Counts

4 → 38

Calls

4 calls:

588.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 l (/.f64 l x))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
172.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
96.0ms	(/.f64 (*.f64 t t) x)
39.0ms	(.f64 (sqrt.f64 (sqrt.f64 2)) (.f64 t (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 4195 to 3474 computations (17.2% saved)

simplify82.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5024	2519

prune202.0ms (0.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	10	10
Picked	0	1	1
Done	1	0	1
Total	111	12	123

Error

0.4b

Counts

123 → 12

Compiler

Compiled 4076 to 2436 computations (40.2% saved)

regimes3.5s (15.3%)

Accuracy

Total 8.4b remaining (95.6%)

Threshold costs 0b (0%)

Compiler

Compiled 27779 to 20417 computations (26.5% saved)

bsearch552.0ms (2.4%)

Steps

Iters	Range		Point
9	4.130901097543475e+106	4.9946944449319984e+113	1.7408606400845876e+113
7	2.7447438050822073e-160	2.449231788390836e-158	2.7803948899544386e-160
9	-5.778300334400232e-299	-2.9706123550469455e-308	-1.037946830000933e-300
9	-1.341456951129372e-119	-1.2087920055378192e-124	-1.2243070715583163e-124
7	-3.649239608667116e+94	-6.411083230629708e+92	-3.1493377557846525e+94

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	220	277
1	220	277

end0.0ms (0%)

sample5.8s (25.6%)

Algorithm

1×

intervals

Results

446.0ms	5311×	body	128	valid
366.0ms	1125×	body	1024	valid
262.0ms	831×	body	1024	nan
231.0ms	943×	body	512	valid
119.0ms	1521×	body	128	nan
117.0ms	512×	body	512	nan
97.0ms	564×	body	256	valid
49.0ms	316×	body	256	nan
23.0ms	57×	body	2048	valid

Compiler

Compiled 4059 to 3013 computations (25.8% saved)

Details

analyze1.3s (5.7%)

sample62.0ms (0.3%)

simplify89.0ms (0.4%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite283.0ms (1.2%)

series6.4s (28%)

simplify102.0ms (0.4%)

prune336.0ms (1.5%)

localize23.0ms (0.1%)

rewrite177.0ms (0.8%)

series965.0ms (4.2%)

simplify101.0ms (0.4%)

prune205.0ms (0.9%)

localize27.0ms (0.1%)

rewrite177.0ms (0.8%)

series882.0ms (3.9%)

simplify83.0ms (0.4%)

prune182.0ms (0.8%)

localize30.0ms (0.1%)

rewrite235.0ms (1%)

series974.0ms (4.3%)

simplify82.0ms (0.4%)

prune202.0ms (0.9%)

regimes3.5s (15.3%)

bsearch552.0ms (2.4%)

simplify6.0ms (0%)

end0.0ms (0%)

sample5.8s (25.6%)

Profiling