Details

analyze164.0ms (3.8%)

Algorithm

1×

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
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

Compiler

Compiled 11 to 11 computations (0% saved)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	33×	body	128	nan
0.0ms	6×	body	128	invalid

Compiler

Compiled 21 to 24 computations (-14.3% saved)

simplify99.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	29	12
1	29	12

prune5.0ms (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

0.1b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize7.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 y (sqrt.f64 z))
0.0b	(+.f64 x (*.f64 y (sqrt.f64 z)))
0.0b	(+.f64 x (*.f64 y (sqrt.f64 z)))
0.2b	(*.f64 y (sqrt.f64 z))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_7261`
6×	`associate-r_binary64_7179`
5×	`*-un-lft-identity_binary64_7239` `add-cube-cbrt_binary64_7274`
4×	`sqrt-prod_binary64_7255` `add-exp-log_binary64_7277` `add-log-exp_binary64_7278` `pow1_binary64_7300` `add-cbrt-cube_binary64_7275`
3×	`associate-l_binary64_7180`
2×	`unswap-sqr_binary64_7207`
1×	`flip-+_binary64_7213` `flip3-+_binary64_7242` `cbrt-unprod_binary64_7272` `pow-prod-down_binary64_7310` `*-commutative_binary64_7170` `prod-exp_binary64_7288` `+-commutative_binary64_7169` `sum-log_binary64_7330`

Counts

2 → 33

Calls

4 calls:

5.0ms	(*.f64 y (sqrt.f64 z))
3.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
0.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
0.0ms	(*.f64 y (sqrt.f64 z))

series146.0ms (3.3%)

Counts

2 → 21

Calls

2 calls:

95.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
50.0ms	(*.f64 y (sqrt.f64 z))

Compiler

Compiled 299 to 303 computations (-1.3% saved)

simplify90.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4832	481
1	4832	481

prune63.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	48	6	54
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	48	7	55

Error

0.0b

Counts

55 → 7

Compiler

Compiled 661 to 278 computations (57.9% saved)

localize9.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
0.1b	(sqrt.f64 (sqrt.f64 z))
0.1b	(sqrt.f64 (sqrt.f64 z))
0.0b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))
0.1b	(sqrt.f64 (sqrt.f64 z))
0.1b	(sqrt.f64 (sqrt.f64 z))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_7255`
25×	`add-sqr-sqrt_binary64_7261`
18×	`associate-r_binary64_7179`
15×	`*-un-lft-identity_binary64_7239` `pow1_binary64_7300` `add-cube-cbrt_binary64_7274`
11×	`add-exp-log_binary64_7277` `add-cbrt-cube_binary64_7275`
8×	`sqrt-pow1_binary64_7257`
4×	`pow1/2_binary64_7319` `rem-sqrt-square_binary64_7252` `add-log-exp_binary64_7278` `cbrt-unprod_binary64_7272` `pow-prod-down_binary64_7310` `prod-exp_binary64_7288` `associate-l_binary64_7180`
3×	`unswap-sqr_binary64_7207`
2×	`*-commutative_binary64_7170`

Counts

4 → 88

Calls

8 calls:

10.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
7.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
2.0ms	(sqrt.f64 (sqrt.f64 z))
2.0ms	(sqrt.f64 (sqrt.f64 z))
0.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))

series281.0ms (6.5%)

Counts

4 → 18

Calls

4 calls:

137.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
55.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
45.0ms	(sqrt.f64 (sqrt.f64 z))
45.0ms	(sqrt.f64 (sqrt.f64 z))

Compiler

Compiled 459 to 429 computations (6.5% saved)

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5186	879

prune104.0ms (2.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	102	4	106
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	105	8	113

Error

Counts

113 → 8

Compiler

Compiled 1733 to 641 computations (63% saved)

localize13.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))
0.3b	(*.f64 y (pow.f64 z 1/4))
0.1b	(sqrt.f64 (sqrt.f64 z))
0.0b	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z))))
0.0b	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z))))
0.1b	(sqrt.f64 (sqrt.f64 z))
0.3b	(*.f64 y (pow.f64 z 1/4))
0.3b	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`sqrt-prod_binary64_7255` `add-exp-log_binary64_7277` `add-sqr-sqrt_binary64_7261`
16×	`associate-r_binary64_7179`
12×	`*-un-lft-identity_binary64_7239` `add-cube-cbrt_binary64_7274`
11×	`add-cbrt-cube_binary64_7275`
10×	`prod-exp_binary64_7288`
8×	`pow1_binary64_7300`
6×	`add-log-exp_binary64_7278`
4×	`cbrt-unprod_binary64_7272` `sqrt-pow1_binary64_7257` `associate-l_binary64_7180` `unpow-prod-down_binary64_7318`
3×	`unswap-sqr_binary64_7207`
2×	`pow1/2_binary64_7319` `rem-sqrt-square_binary64_7252` `sqr-pow_binary64_7211` `pow-to-exp_binary64_7308` `pow-exp_binary64_7307` `*-commutative_binary64_7170`
1×	`flip-+_binary64_7213` `flip3-+_binary64_7242` `pow-prod-down_binary64_7310` `+-commutative_binary64_7169` `sum-log_binary64_7330`

Counts

4 → 80

Calls

8 calls:

9.0ms	(*.f64 y (pow.f64 z 1/4))
9.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))
4.0ms	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z))))
2.0ms	(sqrt.f64 (sqrt.f64 z))
0.0ms	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z))))

series375.0ms (8.6%)

Counts

4 → 30

Calls

4 calls:

162.0ms	(*.f64 y (pow.f64 z 1/4))
107.0ms	(+.f64 x (.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z))))
62.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 z)))
43.0ms	(sqrt.f64 (sqrt.f64 z))

Compiler

Compiled 632 to 612 computations (3.2% saved)

simplify64.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5088	1221

prune118.0ms (2.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	111	7	118

Error

Counts

118 → 7

Compiler

Compiled 1790 to 1001 computations (44.1% saved)

localize19.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
0.1b	(sqrt.f64 (sqrt.f64 z))
0.1b	(sqrt.f64 (sqrt.f64 z))
0.0b	(+.f64 x (.f64 (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))))
0.1b	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
0.3b	(.f64 (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
0.3b	(*.f64 y (pow.f64 z 1/4))
0.3b	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`sqrt-prod_binary64_7255`
35×	`add-exp-log_binary64_7277`
31×	`associate-r_binary64_7179`
26×	`add-sqr-sqrt_binary64_7261`
22×	`prod-exp_binary64_7288`
20×	`add-cbrt-cube_binary64_7275`
18×	`*-un-lft-identity_binary64_7239` `add-cube-cbrt_binary64_7274`
14×	`pow1_binary64_7300`
10×	`cbrt-unprod_binary64_7272`
9×	`sqrt-pow1_binary64_7257`
5×	`associate-l_binary64_7180`
4×	`add-log-exp_binary64_7278` `pow-prod-down_binary64_7310` `unpow-prod-down_binary64_7318`
3×	`pow1/2_binary64_7319` `rem-sqrt-square_binary64_7252` `pow-to-exp_binary64_7308` `pow-exp_binary64_7307` `unswap-sqr_binary64_7207` `*-commutative_binary64_7170`
2×	`sqr-pow_binary64_7211`

Counts

4 → 109

Calls

8 calls:

16.0ms	(.f64 (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
11.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
6.0ms	(*.f64 y (pow.f64 z 1/4))
3.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))
0.0ms	(+.f64 x (.f64 (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))))

series479.0ms (11%)

Counts

4 → 21

Calls

4 calls:

198.0ms	(.f64 (.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
165.0ms	(*.f64 y (pow.f64 z 1/4))
69.0ms	(.f64 (.f64 (*.f64 y (pow.f64 z 1/4)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z)))) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))
47.0ms	(sqrt.f64 (sqrt.f64 (sqrt.f64 z)))

Compiler

Compiled 749 to 652 computations (13% saved)

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5058	1684

prune141.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	130	7	137

Error

Counts

137 → 7

Compiler

Compiled 2753 to 1273 computations (53.8% saved)

simplify14.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	280	696
1	280	696

regimes301.0ms (6.9%)

Compiler: Compiled 2610 to 2058 computations (21.1% saved)

bsearch0.0ms (0%)

regimes226.0ms (5.2%)

Compiler: Compiled 78 to 156 computations (-100% saved)

bsearch109.0ms (2.5%)

Steps

Iters	Range		Point
11	872721941259859.6	2.6843366886188724e+45	3.603416283246761e+22
9	-3.8006714107398703e-48	-8.859351271308502e-56	-5.276988727068237e-51
7	-5.248502515652399e-23	-1.4573664450594664e-24	-4.812826712146534e-24
7	-8.019488011978219e+27	-2.3185226113522465e+26	-2.8447717318394253e+26

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes32.0ms (0.7%)

Compiler: Compiled 24 to 69 computations (-187.5% saved)

bsearch0.0ms (0%)

regimes26.0ms (0.6%)

Compiler: Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes24.0ms (0.6%)

Accuracy

Total 0.1b remaining (86.1%)

Threshold costs 0.1b (86.1%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch4.0ms (0.1%)

Compiler: Compiled 50 to 48 computations (4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	59
1	51	59

end0.0ms (0%)

sample1.1s (25.7%)

Algorithm

1×

intervals

Results

310.0ms	7999×	body	128	valid
39.0ms	1036×	body	128	nan
15.0ms	401×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 481 to 393 computations (18.3% saved)

Pareto

0.5167242733825319

Details

analyze164.0ms (3.8%)

sample21.0ms (0.5%)

simplify99.0ms (2.3%)

prune5.0ms (0.1%)

localize7.0ms (0.2%)

rewrite11.0ms (0.2%)

series146.0ms (3.3%)

simplify90.0ms (2.1%)

prune63.0ms (1.4%)

localize9.0ms (0.2%)

rewrite28.0ms (0.6%)

series281.0ms (6.5%)

simplify88.0ms (2%)

prune104.0ms (2.4%)

localize13.0ms (0.3%)

rewrite30.0ms (0.7%)

series375.0ms (8.6%)

simplify64.0ms (1.5%)

prune118.0ms (2.7%)

localize19.0ms (0.4%)

rewrite48.0ms (1.1%)

series479.0ms (11%)

simplify98.0ms (2.2%)

prune141.0ms (3.2%)

simplify14.0ms (0.3%)

regimes301.0ms (6.9%)

bsearch0.0ms (0%)

regimes226.0ms (5.2%)

bsearch109.0ms (2.5%)

regimes32.0ms (0.7%)

bsearch0.0ms (0%)

regimes26.0ms (0.6%)

bsearch0.0ms (0%)

regimes24.0ms (0.6%)

bsearch4.0ms (0.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (25.7%)

Profiling