Details

analyze1.8s (6.2%)

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)

sample105.0ms (0.4%)

Algorithm

1×

intervals

Results

22.0ms	173×	body	128	valid
15.0ms	31×	body	1024	valid
14.0ms	38×	body	512	valid
13.0ms	27×	body	1024	nan
10.0ms	27×	body	512	nan
6.0ms	46×	body	128	nan
3.0ms	13×	body	256	valid
1.0ms	6×	body	256	nan
1.0ms	1×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify133.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	5192	41

prune7.0ms (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

43.1b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize38.0ms (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)
12.3b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
20.8b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite130.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

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

Counts

4 → 80

Calls

4 calls:

40.0ms	(/.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))))
31.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
31.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
10.0ms	(*.f64 (sqrt.f64 2) t)

series6.5s (22.4%)

Counts

4 → 63

Calls

4 calls:

3.1s	(/.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))))
2.1s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
1.2s	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
59.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 7703 to 6504 computations (15.6% saved)

simplify171.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5218	8369

prune865.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	135	8	143
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	8	144

Error

5.0b

Counts

144 → 8

Compiler

Compiled 7262 to 4628 computations (36.3% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.2b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.3b	(/.f64 (*.f64 l l) x)
10.0b	(/.f64 (*.f64 t t) x)
26.4b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite70.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
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×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94` `flip-+_binary64_52` `flip3-+_binary64_81`
2×	`frac-add_binary64_86` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-r/_binary64_20` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158` `sum-log_binary64_169`

Counts

4 → 70

Calls

4 calls:

24.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
13.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
9.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(/.f64 (*.f64 l l) x)

series1.3s (4.6%)

Counts

4 → 38

Calls

4 calls:

828.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
249.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
125.0ms	(/.f64 (*.f64 l l) x)
122.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 2165 to 1832 computations (15.4% saved)

simplify144.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4964	1998
1	4964	1998

prune294.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	104	12	116

Error

0.4b

Counts

116 → 12

Compiler

Compiled 3536 to 2076 computations (41.3% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))
3.2b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
10.0b	(/.f64 (*.f64 t t) x)
26.4b	(sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x)))))

rewrite128.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`associate-*r/_binary64_20`
12×	`frac-add_binary64_86`
11×	`add-log-exp_binary64_117`
9×	`add-cbrt-cube_binary64_114` `flip-+_binary64_52` `add-exp-log_binary64_116` `flip3-+_binary64_81`
8×	`add-sqr-sqrt_binary64_100` `sqrt-div_binary64_95`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139`
4×	`frac-times_binary64_88` `associate-*l/_binary64_21` `sum-log_binary64_169`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129`
1×	`sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `associate-+r+_binary64_10` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 72

Calls

4 calls:

43.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x)))))
40.0ms	(+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))
13.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
10.0ms	(/.f64 (*.f64 t t) x)

series1.7s (5.9%)

Counts

4 → 50

Calls

4 calls:

720.0ms	(+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))
596.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x)))))
256.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
128.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 2679 to 2256 computations (15.8% saved)

simplify173.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4994	3889
1	4994	3889

prune354.0ms (1.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	121	13	134

Error

0.4b

Counts

134 → 13

Compiler

Compiled 4925 to 2426 computations (50.7% saved)

localize39.0ms (0.1%)

Local error

Found 4 expressions with local error:

10.0b	(/.f64 (*.f64 t t) x)
10.0b	(/.f64 (*.f64 t t) x)
26.4b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t)))))
26.4b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t)))))

rewrite71.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

15.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t)))))
15.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t)))))
9.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(/.f64 (*.f64 t t) x)

series2.7s (9.2%)

Counts

4 → 60

Calls

4 calls:

1.2s	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t)))))
1.1s	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (/.f64 l (/.f64 x l)) (.f64 t t)))))
163.0ms	(/.f64 (*.f64 t t) x)
161.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 7002 to 5350 computations (23.6% saved)

simplify188.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5032	4310

prune655.0ms (2.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	135	14	149

Error

0.4b

Counts

149 → 14

Compiler

Compiled 7770 to 3621 computations (53.4% saved)

regimes3.3s (11.4%)

Accuracy

Total 9.8b remaining (96.4%)

Threshold costs 0b (0%)

Compiler

Compiled 19903 to 14356 computations (27.9% saved)

bsearch611.0ms (2.1%)

Steps

Iters	Range		Point
8	0.3235610345440489	125.79987750142081	124.71595513294787
9	-8.594646213452616e-250	-3.18881780711917e-259	-8.423808617895155e-250
6	-7.165162097849366e-125	-1.0374509790245683e-125	-1.0501925897887986e-125
9	-5.810499564474157e+121	-4.836023599108778e+112	-1.493328393148849e+117

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	124	188
1	124	188

end0.0ms (0%)

sample7.3s (25.4%)

Algorithm

1×

intervals

Results

749.0ms	5376×	body	128	valid
589.0ms	1091×	body	1024	valid
402.0ms	774×	body	1024	nan
352.0ms	896×	body	512	valid
198.0ms	525×	body	512	nan
192.0ms	1487×	body	128	nan
152.0ms	571×	body	256	valid
66.0ms	267×	body	256	nan
45.0ms	66×	body	2048	valid

Compiler

Compiled 2960 to 2122 computations (28.3% saved)

Details

analyze1.8s (6.2%)

sample105.0ms (0.4%)

simplify133.0ms (0.5%)

prune7.0ms (0%)

localize38.0ms (0.1%)

rewrite130.0ms (0.5%)

series6.5s (22.4%)

simplify171.0ms (0.6%)

prune865.0ms (3%)

localize39.0ms (0.1%)

rewrite70.0ms (0.2%)

series1.3s (4.6%)

simplify144.0ms (0.5%)

prune294.0ms (1%)

localize45.0ms (0.2%)

rewrite128.0ms (0.4%)

series1.7s (5.9%)

simplify173.0ms (0.6%)

prune354.0ms (1.2%)

localize39.0ms (0.1%)

rewrite71.0ms (0.2%)

series2.7s (9.2%)

simplify188.0ms (0.7%)

prune655.0ms (2.3%)

regimes3.3s (11.4%)

bsearch611.0ms (2.1%)

simplify8.0ms (0%)

end0.0ms (0%)

sample7.3s (25.4%)

Profiling