Details

analyze1.6s (4.4%)

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)

sample123.0ms (0.3%)

Algorithm

1×

intervals

Results

22.0ms	170×	body	128	valid
21.0ms	43×	body	1024	valid
20.0ms	41×	body	1024	nan
9.0ms	23×	body	512	valid
8.0ms	66×	body	128	nan
8.0ms	21×	body	512	nan
4.0ms	17×	body	256	valid
3.0ms	11×	body	256	nan
2.0ms	3×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify108.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5192	41

prune10.0ms (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

37.7b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize34.0ms (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)
10.8b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
15.3b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite393.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

37.5b

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	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
29.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
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))))
5.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3564 to 2030 computations (43% saved)

series5.2s (14.3%)

Error

6.0b

Counts

4 → 58

Calls

4 calls:

2.6s	(/.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))))
1.3s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
1.0s	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
57.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 9592 to 7988 computations (16.7% saved)

simplify89.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5155	6025

prune616.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	130	8	138
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	8	139

Error

6.0b

Counts

139 → 8

Compiler

Compiled 5815 to 3553 computations (38.9% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.9b	(/.f64 (*.f64 t t) x)
10.1b	(/.f64 (.f64 l l) (.f64 x x))
15.4b	(/.f64 (.f64 t t) (.f64 x x))
21.7b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))))))

rewrite302.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

5.9b

Rules

33×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
20×	`associate-*r/_binary64_20`
16×	`frac-add_binary64_86`
10×	`sqrt-div_binary64_95` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
9×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111`
8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113` `flip3-+_binary64_81` `flip-+_binary64_52` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`add-log-exp_binary64_117`
3×	`sqrt-prod_binary64_94` `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`

Counts

4 → 86

Calls

4 calls:

16.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))))))
11.0ms	(/.f64 (.f64 l l) (.f64 x x))
8.0ms	(/.f64 (.f64 t t) (.f64 x x))
8.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 5815 to 1665 computations (71.4% saved)

series1.8s (4.9%)

Error

0.3b

Counts

4 → 39

Calls

4 calls:

1.2s	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x)))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (.f64 x x)))))))
172.0ms	(/.f64 (.f64 t t) (.f64 x x))
157.0ms	(/.f64 (.f64 l l) (.f64 x x))
140.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 6795 to 5116 computations (24.7% saved)

simplify187.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4970	4880
1	4970	4880

prune346.0ms (1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	119	6	125
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	123	10	133

Error

0.2b

Counts

133 → 10

Compiler

Compiled 7316 to 2897 computations (60.4% saved)

localize41.0ms (0.1%)

Local error

Found 4 expressions with local error:

15.4b	(/.f64 (.f64 t t) (.f64 x x))
15.4b	(/.f64 (.f64 t t) (.f64 x x))
21.7b	(sqrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
21.7b	(sqrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))

rewrite580.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

48×	`associate-*r/_binary64_20`
44×	`frac-add_binary64_86`
28×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `sqrt-div_binary64_95`
22×	`flip3-+_binary64_81` `flip-+_binary64_52`
8×	`add-sqr-sqrt_binary64_100` `prod-exp_binary64_127` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `cbrt-unprod_binary64_111`
6×	`pow1_binary64_139` `add-cube-cbrt_binary64_113` `sqrt-prod_binary64_94` `*-un-lft-identity_binary64_78`
4×	`add-log-exp_binary64_117`
2×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `times-frac_binary64_84` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-/r_binary64_22`

Counts

4 → 96

Calls

4 calls:

32.0ms	(sqrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
32.0ms	(sqrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
14.0ms	(/.f64 (.f64 t t) (.f64 x x))
13.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 12148 to 2404 computations (80.2% saved)

series4.7s (13%)

Error

0.2b

Counts

4 → 60

Calls

4 calls:

2.0s	(sqrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
2.0s	(sqrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
177.0ms	(/.f64 (.f64 t t) (.f64 x x))
100.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 20252 to 13781 computations (32% saved)

simplify177.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5055	11418

prune793.0ms (2.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	156	10	166

Error

0.2b

Counts

166 → 10

Compiler

Compiled 16962 to 5756 computations (66.1% saved)

localize57.0ms (0.2%)

Local error

Found 4 expressions with local error:

15.4b	(/.f64 (.f64 t t) (.f64 x x))
15.4b	(/.f64 (.f64 t t) (.f64 x x))
22.5b	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
22.5b	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))

rewrite517.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

48×	`associate-*r/_binary64_20`
44×	`frac-add_binary64_86`
28×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `cbrt-div_binary64_110`
22×	`flip3-+_binary64_81` `flip-+_binary64_52`
8×	`prod-exp_binary64_127` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `cbrt-unprod_binary64_111`
6×	`add-cube-cbrt_binary64_113` `cbrt-prod_binary64_109` `add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
4×	`pow1_binary64_139` `add-log-exp_binary64_117`
2×	`pow1/3_binary64_160` `frac-2neg_binary64_89` `times-frac_binary64_84` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-/r_binary64_22`

Counts

4 → 92

Calls

4 calls:

25.0ms	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
19.0ms	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
11.0ms	(/.f64 (.f64 t t) (.f64 x x))
7.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 11820 to 2320 computations (80.4% saved)

series4.6s (12.7%)

Error

0.2b

Counts

4 → 50

Calls

4 calls:

2.1s	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
1.9s	(cbrt.f64 (+.f64 (.f64 2 (+.f64 (/.f64 (.f64 l l) x) (+.f64 (.f64 t t) (/.f64 (.f64 l l) (.f64 x x))))) (.f64 4 (+.f64 (/.f64 (.f64 t t) x) (/.f64 (.f64 t t) (*.f64 x x))))))
153.0ms	(/.f64 (.f64 t t) (.f64 x x))
152.0ms	(/.f64 (.f64 t t) (.f64 x x))

Compiler

Compiled 15976 to 10744 computations (32.7% saved)

simplify221.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4987	9970
1	4987	9970

prune715.0ms (2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	142	0	142
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	142	10	152

Error

0.2b

Counts

152 → 10

Compiler

Compiled 14776 to 4543 computations (69.3% saved)

regimes3.8s (10.5%)

Accuracy

Total 10.6b remaining (95.5%)

Threshold costs 0b (0%)

Compiler

Compiled 33813 to 21617 computations (36.1% saved)

bsearch1.1s (3%)

Steps

Iters	Range		Point
6	15416880.864465715	78701229.42658019	77477067.12571414
9	1.5326910901157542e-222	3.0067332268856036e-215	1.5653638338130407e-222
10	1.1907512310747845e-302	3.365231874819948e-288	3.2882651861996704e-288
4	-2.709141374674036e-220	-1.7475945174360627e-220	-2.6783763174270457e-220
9	-1.8644078173527896e-154	-2.918498801633069e-160	-2.97191195562455e-160
7	-124.11376151596332	-7.607530233839697	-123.10441277465658

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify15.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	237	419
1	237	419

end0.0ms (0%)

sample8.1s (22.4%)

Algorithm

1×

intervals

Results

598.0ms	5241×	body	128	valid
549.0ms	1212×	body	1024	valid
352.0ms	814×	body	1024	nan
312.0ms	936×	body	512	valid
176.0ms	517×	body	512	nan
172.0ms	1507×	body	128	nan
125.0ms	543×	body	256	valid
53.0ms	253×	body	256	nan
39.0ms	68×	body	2048	valid

Compiler

Compiled 5030 to 3275 computations (34.9% saved)

Details

analyze1.6s (4.4%)

sample123.0ms (0.3%)

simplify108.0ms (0.3%)

prune10.0ms (0%)

localize34.0ms (0.1%)

rewrite393.0ms (1.1%)

series5.2s (14.3%)

simplify89.0ms (0.2%)

prune616.0ms (1.7%)

localize31.0ms (0.1%)

rewrite302.0ms (0.8%)

series1.8s (4.9%)

simplify187.0ms (0.5%)

prune346.0ms (1%)

localize41.0ms (0.1%)

rewrite580.0ms (1.6%)

series4.7s (13%)

simplify177.0ms (0.5%)

prune793.0ms (2.2%)

localize57.0ms (0.2%)

rewrite517.0ms (1.4%)

series4.6s (12.7%)

simplify221.0ms (0.6%)

prune715.0ms (2%)

regimes3.8s (10.5%)

bsearch1.1s (3%)

simplify15.0ms (0%)

end0.0ms (0%)

sample8.1s (22.4%)

Profiling