Details

analyze236.0ms (4.1%)

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
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
10.1%	64.7%	25.1%	8
17.2%	32.8%	50.1%	9
23%	26.9%	50.1%	10
26.8%	23.1%	50.1%	11
31.6%	18.3%	50.1%	12
35.2%	14.7%	50.1%	13
37.5%	12.4%	50.1%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample21.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify239.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	1363	18
1	1363	18

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
0.0b	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
0.1b	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
0.1b	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_11775` `add-log-exp_binary64_11814`
15×	`add-sqr-sqrt_binary64_11797`
12×	`log-prod_binary64_11861`
11×	`add-cube-cbrt_binary64_11810`
7×	`pow1_binary64_11836`
6×	`distribute-rgt-in_binary64_11725` `add-cbrt-cube_binary64_11811` `add-exp-log_binary64_11813` `diff-log_binary64_11867` `associate--r+_binary64_11711` `distribute-lft-in_binary64_11724`
5×	`cancel-sign-sub-inv_binary64_11741`
4×	`associate-l_binary64_11716` `associate-r_binary64_11715` `sum-log_binary64_11866`
3×	`distribute-lft-out_binary64_11726` `sub-neg_binary64_11768`
2×	`flip3-+_binary64_11778` `flip3--_binary64_11779` `associate-*l/_binary64_11718` `flip-+_binary64_11749` `associate-+l+_binary64_11708` `flip--_binary64_11750` `distribute-lft-out--_binary64_11727` `associate-+l-_binary64_11710`
1×	`associate--l-_binary64_11713` `pow-prod-down_binary64_11846` `*-commutative_binary64_11706` `prod-exp_binary64_11824` `associate--l+_binary64_11712` `cbrt-unprod_binary64_11808` `log-pow_binary64_11864` `+-commutative_binary64_11705` `unswap-sqr_binary64_11743` `difference-of-squares_binary64_11744`

Counts

4 → 83

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
7.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
5.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

series431.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
97.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
83.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
66.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify95.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4955	1643
1	4955	1643

prune205.0ms (3.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	7	96

Merged error: 0.0b

Counts

96 → 7

Compiler

Compiled 3617 to 2382 computations (34.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
0.3b	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`log-prod_binary64_11861`
36×	`distribute-rgt-in_binary64_11725` `distribute-lft-in_binary64_11724`
30×	`cbrt-prod_binary64_11806`
26×	`*-un-lft-identity_binary64_11775` `add-sqr-sqrt_binary64_11797`
24×	`associate-+l+_binary64_11708` `add-cube-cbrt_binary64_11810`
12×	`associate-+r+_binary64_11707`
10×	`associate-*l/_binary64_11718`
7×	`pow1_binary64_11836`
6×	`flip3-+_binary64_11778` `flip-+_binary64_11749` `add-cbrt-cube_binary64_11811` `add-exp-log_binary64_11813` `add-log-exp_binary64_11814`
5×	`associate-r_binary64_11715`
4×	`associate-l_binary64_11716` `frac-add_binary64_11783`
3×	`pow1/3_binary64_11857`
2×	`distribute-lft-out_binary64_11726` `log-pow_binary64_11864`
1×	`pow-prod-down_binary64_11846` `*-commutative_binary64_11706` `prod-exp_binary64_11824` `cbrt-unprod_binary64_11808` `+-commutative_binary64_11705` `unswap-sqr_binary64_11743` `sum-log_binary64_11866`

Counts

4 → 109

Calls

4 calls:

16.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
9.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series1.5s (26%)

Counts

4 → 12

Calls

4 calls:

765.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
422.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
157.0ms	(cbrt.f64 y)
144.0ms	(cbrt.f64 y)

simplify107.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4900	1857
1	4900	1857

prune199.0ms (3.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	121	7	128

Merged error: 0b

Counts

128 → 7

Compiler

Compiled 4118 to 2480 computations (39.8% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (pow.f64 y 2/3))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 (cbrt.f64 y))
6.1b	(pow.f64 y 2/3)

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`cbrt-prod_binary64_11806`
11×	`add-cube-cbrt_binary64_11810` `*-un-lft-identity_binary64_11775` `add-sqr-sqrt_binary64_11797`
6×	`unpow-prod-down_binary64_11854`
5×	`pow1_binary64_11836` `add-exp-log_binary64_11813`
4×	`add-cbrt-cube_binary64_11811` `add-log-exp_binary64_11814`
3×	`pow-unpow_binary64_11852` `pow1/3_binary64_11857`
2×	`sqr-pow_binary64_11747`
1×	`pow-to-exp_binary64_11844` `pow-pow_binary64_11847` `pow-exp_binary64_11843`

Counts

4 → 57

Calls

4 calls:

3.0ms	(pow.f64 y 2/3)
2.0ms	(cbrt.f64 (pow.f64 y 2/3))
2.0ms	(cbrt.f64 (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

series681.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(cbrt.f64 (cbrt.f64 y))
171.0ms	(cbrt.f64 y)
149.0ms	(cbrt.f64 (pow.f64 y 2/3))
147.0ms	(pow.f64 y 2/3)

simplify60.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4784	508
1	4784	508

prune123.0ms (2.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	69	7	76

Merged error: 0b

Counts

76 → 7

Compiler

Compiled 2495 to 1567 computations (37.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2)))))
0.1b	(+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))) y)
0.4b	(*.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2)))
0.4b	(.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_11775`
14×	`sqrt-div_binary64_11792`
13×	`add-sqr-sqrt_binary64_11797`
12×	`pow1_binary64_11836`
11×	`associate-l_binary64_11716` `add-cbrt-cube_binary64_11811` `add-exp-log_binary64_11813` `add-log-exp_binary64_11814`
10×	`associate-*r/_binary64_11717`
9×	`sqrt-prod_binary64_11791` `add-cube-cbrt_binary64_11810`
8×	`flip3-+_binary64_11778` `flip-+_binary64_11749` `associate-r_binary64_11715`
4×	`pow-prod-down_binary64_11846` `prod-exp_binary64_11824` `frac-times_binary64_11785` `cbrt-unprod_binary64_11808`
3×	`distribute-lft-out_binary64_11726`
2×	`associate-l/_binary64_11718` `-commutative_binary64_11706` `associate-+l+_binary64_11708` `diff-log_binary64_11867` `unswap-sqr_binary64_11743` `sum-log_binary64_11866` `sub-neg_binary64_11768` `cancel-sign-sub-inv_binary64_11741`
1×	`flip3--_binary64_11779` `flip--_binary64_11750` `log-pow_binary64_11864` `+-commutative_binary64_11705` `associate-+l-_binary64_11710`

Counts

4 → 84

Calls

4 calls:

14.0ms	(.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))
11.0ms	(*.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2)))
6.0ms	(+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))) y)
3.0ms	(-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2)))))

series402.0ms (7%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))
85.0ms	(+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))) y)
79.0ms	(*.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2)))
64.0ms	(-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2)))))

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5742	1792

prune106.0ms (1.8%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	96	7	103

Merged error: 0b

Counts

103 → 7

Compiler

Compiled 2123 to 1309 computations (38.3% saved)

regimes97.0ms (1.7%)

Compiler: Compiled 815 to 646 computations (20.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	18
1	64	18

end0.0ms (0%)

sample968.0ms (16.9%)

Algorithm

1×

intervals

Results

394.0ms	7999×	body	128	valid
2.0ms	39×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 190 to 152 computations (20% saved)

Details

analyze236.0ms (4.1%)

sample21.0ms (0.4%)

simplify239.0ms (4.2%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite35.0ms (0.6%)

series431.0ms (7.5%)

simplify95.0ms (1.7%)

prune205.0ms (3.6%)

localize15.0ms (0.3%)

rewrite42.0ms (0.7%)

series1.5s (26%)

simplify107.0ms (1.9%)

prune199.0ms (3.5%)

localize29.0ms (0.5%)

rewrite14.0ms (0.2%)

series681.0ms (11.9%)

simplify60.0ms (1.1%)

prune123.0ms (2.1%)

localize12.0ms (0.2%)

rewrite44.0ms (0.8%)

series402.0ms (7%)

simplify67.0ms (1.2%)

prune106.0ms (1.8%)

regimes97.0ms (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample968.0ms (16.9%)

Profiling