Details

analyze163.0ms (4.9%)

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)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	28×	body	128	nan
0.0ms	12×	body	128	invalid

Compiler

Compiled 21 to 24 computations (-14.3% saved)

simplify163.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	29	12
1	29	12

prune7.0ms (0.2%)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 16 computations (0% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_7175`
6×	`associate-r_binary64_7096`
5×	`add-cube-cbrt_binary64_7186` `*-un-lft-identity_binary64_7154`
4×	`pow1_binary64_7212` `add-cbrt-cube_binary64_7187` `add-log-exp_binary64_7190` `sqrt-prod_binary64_7169` `add-exp-log_binary64_7189`
3×	`associate-l_binary64_7097`
2×	`unswap-sqr_binary64_7122`
1×	`flip-+_binary64_7128` `+-commutative_binary64_7086` `flip3-+_binary64_7157` `*-commutative_binary64_7087` `sum-log_binary64_7242` `cbrt-unprod_binary64_7184` `pow-prod-down_binary64_7222` `prod-exp_binary64_7200`

Counts

2 → 33

Calls

2 calls:

6.0ms	(*.f64 y (sqrt.f64 z))
4.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))

series119.0ms (3.6%)

Counts

2 → 6

Calls

2 calls:

62.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
57.0ms	(*.f64 y (sqrt.f64 z))

simplify60.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5064	474

prune42.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Merged error: 0.0b

Counts

40 → 7

Compiler

Compiled 614 to 288 computations (53.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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)))

rewrite34.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_7169`
25×	`add-sqr-sqrt_binary64_7175`
18×	`associate-r_binary64_7096`
15×	`pow1_binary64_7212` `add-cube-cbrt_binary64_7186` `*-un-lft-identity_binary64_7154`
11×	`add-cbrt-cube_binary64_7187` `add-exp-log_binary64_7189`
8×	`sqrt-pow1_binary64_7171`
4×	`rem-sqrt-square_binary64_7167` `pow1/2_binary64_7231` `add-log-exp_binary64_7190` `associate-l_binary64_7097` `cbrt-unprod_binary64_7184` `pow-prod-down_binary64_7222` `prod-exp_binary64_7200`
3×	`unswap-sqr_binary64_7122`
2×	`*-commutative_binary64_7087`

Counts

4 → 88

Calls

4 calls:

12.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
8.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
2.0ms	(sqrt.f64 (sqrt.f64 z))
2.0ms	(sqrt.f64 (sqrt.f64 z))

series368.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(sqrt.f64 (sqrt.f64 z))
107.0ms	(sqrt.f64 (sqrt.f64 z))
87.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
61.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

simplify64.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4918	1032
1	4918	1032

prune100.0ms (3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	4	1	5
Picked	1	0	1
Done	0	1	1
Total	100	7	107

Merged error: 0b

Counts

107 → 7

Compiler

Compiled 1763 to 669 computations (62.1% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`sqrt-prod_binary64_7169`
20×	`add-sqr-sqrt_binary64_7175`
19×	`add-exp-log_binary64_7189`
16×	`associate-r_binary64_7096`
12×	`add-cube-cbrt_binary64_7186` `*-un-lft-identity_binary64_7154`
11×	`add-cbrt-cube_binary64_7187`
10×	`prod-exp_binary64_7200`
8×	`pow1_binary64_7212`
6×	`add-log-exp_binary64_7190`
4×	`sqrt-pow1_binary64_7171` `associate-l_binary64_7097` `cbrt-unprod_binary64_7184`
3×	`unpow-prod-down_binary64_7230` `unswap-sqr_binary64_7122`
2×	`pow-exp_binary64_7219` `rem-sqrt-square_binary64_7167` `pow1/2_binary64_7231` `*-commutative_binary64_7087` `pow-to-exp_binary64_7220`
1×	`flip-+_binary64_7128` `+-commutative_binary64_7086` `flip3-+_binary64_7157` `sum-log_binary64_7242` `sqr-pow_binary64_7126` `pow-prod-down_binary64_7222`

Counts

4 → 80

Calls

4 calls:

10.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))
8.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
4.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4)))
2.0ms	(sqrt.f64 (sqrt.f64 z))

series406.0ms (12.2%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4)))
112.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))
101.0ms	(sqrt.f64 (sqrt.f64 z))
80.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))

simplify86.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4895	1333
1	4895	1333

prune94.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	92	7	99

Merged error: 0b

Counts

99 → 7

Compiler

Compiled 1756 to 932 computations (46.9% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3)))
0.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3))
0.7b	(pow.f64 (sqrt.f64 (sqrt.f64 z)) 3)

rewrite50.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-prod_binary64_7169`
48×	`cbrt-prod_binary64_7182`
36×	`associate-r_binary64_7096` `add-sqr-sqrt_binary64_7175`
30×	`add-cube-cbrt_binary64_7186` `*-un-lft-identity_binary64_7154`
27×	`cube-prod_binary64_7179` `unpow-prod-down_binary64_7230`
14×	`pow1_binary64_7212`
12×	`add-exp-log_binary64_7189`
10×	`add-cbrt-cube_binary64_7187`
5×	`pow-pow_binary64_7223`
4×	`sqrt-pow1_binary64_7171` `add-log-exp_binary64_7190` `associate-l_binary64_7097` `cbrt-unprod_binary64_7184` `pow-prod-down_binary64_7222` `prod-exp_binary64_7200`
3×	`pow-unpow_binary64_7228` `cube-mult_binary64_7181` `sqr-pow_binary64_7126` `unpow3_binary64_7217` `unswap-sqr_binary64_7122`
2×	`pow1/2_binary64_7231` `*-commutative_binary64_7087`
1×	`pow-exp_binary64_7219` `rem-cbrt-cube_binary64_7177` `pow1/3_binary64_7233` `pow-to-exp_binary64_7220` `rem-cube-cbrt_binary64_7176` `sqrt-pow2_binary64_7172`

Counts

4 → 141

Calls

4 calls:

17.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3)))
8.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
5.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 z)) 3)
5.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3))

series390.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 z)) 3)
113.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3))
75.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
59.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3)))

simplify87.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4855	1706
1	4855	1706

prune142.0ms (4.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	153	7	160

Merged error: 0b

Counts

160 → 7

Compiler

Compiled 2862 to 1236 computations (56.8% saved)

regimes107.0ms (3.2%)

Compiler: Compiled 708 to 540 computations (23.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	12
1	12	12

end0.0ms (0%)

sample735.0ms (22.1%)

Algorithm

1×

intervals

Results

320.0ms	8000×	body	128	valid
39.0ms	1020×	body	128	nan
15.0ms	384×	body	128	invalid

Compiler

Compiled 132 to 104 computations (21.2% saved)

Details

analyze163.0ms (4.9%)

sample20.0ms (0.6%)

simplify163.0ms (4.9%)

prune7.0ms (0.2%)

localize6.0ms (0.2%)

rewrite12.0ms (0.4%)

series119.0ms (3.6%)

simplify60.0ms (1.8%)

prune42.0ms (1.3%)

localize9.0ms (0.3%)

rewrite34.0ms (1%)

series368.0ms (11.1%)

simplify64.0ms (1.9%)

prune100.0ms (3%)

localize15.0ms (0.5%)

rewrite31.0ms (0.9%)

series406.0ms (12.2%)

simplify86.0ms (2.6%)

prune94.0ms (2.8%)

localize12.0ms (0.4%)

rewrite50.0ms (1.5%)

series390.0ms (11.7%)

simplify87.0ms (2.6%)

prune142.0ms (4.3%)

regimes107.0ms (3.2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample735.0ms (22.1%)

Profiling