Details

analyze154.0ms (3.7%)

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
25%	74.9%	0.1%	5
37.5%	62.4%	0.1%	6
43.7%	43.7%	12.6%	7
53.1%	34.3%	12.6%	8
57.8%	23.4%	18.8%	9
63.2%	18%	18.8%	10
66%	12.1%	22%	11
68.9%	9.2%	22%	12
70.3%	6.1%	23.5%	13
71.9%	4.6%	23.5%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify157.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	32	10
1	32	10

prune3.0ms (0.1%)

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

Merged error: 3.3b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (*.f64 y y))
3.1b	(.f64 x (+.f64 1 (.f64 y y)))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_15104`
4×	`add-cube-cbrt_binary64_15117` `add-cbrt-cube_binary64_15118` `*-un-lft-identity_binary64_15082` `pow1_binary64_15143` `add-log-exp_binary64_15121` `add-exp-log_binary64_15120`
3×	`associate-l_binary64_15023` `associate-r_binary64_15022`
2×	`flip-+_binary64_15056` `associate-*r/_binary64_15024` `flip3-+_binary64_15085`
1×	`pow-prod-down_binary64_15153` `unswap-sqr_binary64_15050` `sum-log_binary64_15173` `prod-exp_binary64_15131` `distribute-rgt-in_binary64_15032` `distribute-lft-in_binary64_15031` `cbrt-unprod_binary64_15115` `+-commutative_binary64_15012` `*-commutative_binary64_15013`

Counts

2 → 33

Calls

2 calls:

10.0ms	(.f64 x (+.f64 1 (.f64 y y)))
5.0ms	(+.f64 1 (*.f64 y y))

series106.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

66.0ms	(.f64 x (+.f64 1 (.f64 y y)))
39.0ms	(+.f64 1 (*.f64 y y))

simplify116.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	6035	428

prune68.0ms (1.6%)

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: 3.2b

Counts

40 → 7

Compiler

Compiled 515 to 289 computations (43.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (sqrt.f64 (+.f64 1 (.f64 y y))) (sqrt.f64 (+.f64 1 (*.f64 y y))))
3.1b	(sqrt.f64 (+.f64 1 (*.f64 y y)))
3.1b	(sqrt.f64 (+.f64 1 (*.f64 y y)))
3.1b	(.f64 x (.f64 (sqrt.f64 (+.f64 1 (.f64 y y))) (sqrt.f64 (+.f64 1 (.f64 y y)))))

rewrite78.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_15104`
28×	`sqrt-div_binary64_15099`
26×	`pow1_binary64_15143`
24×	`sqrt-prod_binary64_15098`
15×	`add-cube-cbrt_binary64_15117` `*-un-lft-identity_binary64_15082`
14×	`flip-+_binary64_15056` `flip3-+_binary64_15085`
12×	`associate-*r/_binary64_15024`
11×	`add-cbrt-cube_binary64_15118` `add-exp-log_binary64_15120`
10×	`pow1/2_binary64_15162` `sqrt-pow1_binary64_15100`
9×	`associate-l_binary64_15023`
8×	`frac-times_binary64_15092` `swap-sqr_binary64_15049`
7×	`associate-r_binary64_15022`
6×	`pow-prod-down_binary64_15153`
5×	`unswap-sqr_binary64_15050` `pow-prod-up_binary64_15152`
4×	`prod-exp_binary64_15131` `rem-sqrt-square_binary64_15095` `cbrt-unprod_binary64_15115` `add-log-exp_binary64_15121` `associate-*l/_binary64_15025`
3×	`pow-sqr_binary64_15055`
2×	`*-commutative_binary64_15013`
1×	`rem-square-sqrt_binary64_15094` `pow2_binary64_15163` `sqrt-unprod_binary64_15102` `sqr-abs_binary64_15097` `pow-plus_binary64_15145`

Counts

4 → 115

Calls

4 calls:

24.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 1 (.f64 y y))) (sqrt.f64 (+.f64 1 (.f64 y y)))))
23.0ms	(.f64 (sqrt.f64 (+.f64 1 (.f64 y y))) (sqrt.f64 (+.f64 1 (*.f64 y y))))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))

series188.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 1 (.f64 y y))) (sqrt.f64 (+.f64 1 (.f64 y y)))))
43.0ms	(.f64 (sqrt.f64 (+.f64 1 (.f64 y y))) (sqrt.f64 (+.f64 1 (*.f64 y y))))
36.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
34.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))

simplify88.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5040	1648

prune225.0ms (5.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	126	1	127
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	127	7	134

Merged error: 3.2b

Counts

134 → 7

Compiler

Compiled 2264 to 1345 computations (40.6% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (sqrt.f64 (+.f64 1 (.f64 y y))))
0.1b	(.f64 (.f64 x (sqrt.f64 (+.f64 1 (.f64 y y)))) (sqrt.f64 (+.f64 1 (.f64 y y))))
3.1b	(sqrt.f64 (+.f64 1 (*.f64 y y)))
3.1b	(sqrt.f64 (+.f64 1 (*.f64 y y)))

rewrite69.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`sqrt-div_binary64_15099`
17×	`add-sqr-sqrt_binary64_15104`
13×	`sqrt-prod_binary64_15098` `pow1_binary64_15143`
12×	`associate-r_binary64_15022`
11×	`add-cube-cbrt_binary64_15117` `add-cbrt-cube_binary64_15118` `*-un-lft-identity_binary64_15082` `add-exp-log_binary64_15120`
10×	`associate-*r/_binary64_15024`
9×	`flip-+_binary64_15056` `flip3-+_binary64_15085`
4×	`pow-prod-down_binary64_15153` `frac-times_binary64_15092` `prod-exp_binary64_15131` `cbrt-unprod_binary64_15115` `add-log-exp_binary64_15121` `associate-l_binary64_15023`
2×	`unswap-sqr_binary64_15050` `pow1/2_binary64_15162` `sqrt-pow1_binary64_15100` `rem-sqrt-square_binary64_15095` `-commutative_binary64_15013` `associate-l/_binary64_15025`

Counts

4 → 83

Calls

4 calls:

24.0ms	(.f64 (.f64 x (sqrt.f64 (+.f64 1 (.f64 y y)))) (sqrt.f64 (+.f64 1 (.f64 y y))))
19.0ms	(.f64 x (sqrt.f64 (+.f64 1 (.f64 y y))))
6.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
6.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))

series220.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(.f64 x (sqrt.f64 (+.f64 1 (.f64 y y))))
71.0ms	(.f64 (.f64 x (sqrt.f64 (+.f64 1 (.f64 y y)))) (sqrt.f64 (+.f64 1 (.f64 y y))))
33.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
29.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))

simplify177.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	4884	1418
1	4884	1418

prune249.0ms (5.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	95	7	102

Merged error: 3.2b

Counts

102 → 7

Compiler

Compiled 1896 to 1130 computations (40.4% saved)

localize19.0ms (0.5%)

Local error

Found 4 expressions with local error:

3.1b	(sqrt.f64 (+.f64 1 (*.f64 y y)))
3.1b	(sqrt.f64 (+.f64 1 (*.f64 y y)))
3.1b	(sqrt.f64 (+.f64 1 (*.f64 y y)))
3.1b	(.f64 x (.f64 (sqrt.f64 (+.f64 1 (.f64 y y))) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 y y)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 y y)))))))

rewrite107.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`sqrt-div_binary64_15099`
40×	`associate-*r/_binary64_15024`
30×	`flip-+_binary64_15056` `flip3-+_binary64_15085`
28×	`frac-times_binary64_15092`
16×	`pow1_binary64_15143`
13×	`add-cbrt-cube_binary64_15118` `add-exp-log_binary64_15120`
11×	`add-sqr-sqrt_binary64_15104`
9×	`sqrt-prod_binary64_15098`
8×	`add-cube-cbrt_binary64_15117` `-un-lft-identity_binary64_15082` `associate-l/_binary64_15025`
6×	`pow-prod-down_binary64_15153` `prod-exp_binary64_15131` `cbrt-unprod_binary64_15115`
4×	`add-log-exp_binary64_15121`
3×	`pow1/2_binary64_15162` `sqrt-pow1_binary64_15100` `rem-sqrt-square_binary64_15095` `associate-l_binary64_15023`
1×	`-commutative_binary64_15013` `associate-r*_binary64_15022`

Counts

4 → 92

Calls

4 calls:

63.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 1 (.f64 y y))) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 y y)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 y y)))))))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
5.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))

series170.0ms (4%)

Counts

4 → 12

Calls

4 calls:

78.0ms	(.f64 x (.f64 (sqrt.f64 (+.f64 1 (.f64 y y))) (.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 y y)))) (sqrt.f64 (sqrt.f64 (+.f64 1 (.f64 y y)))))))
33.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
30.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))
27.0ms	(sqrt.f64 (+.f64 1 (*.f64 y y)))

simplify125.0ms (3%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5063	1734

prune266.0ms (6.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	104	7	111

Merged error: 3.2b

Counts

111 → 7

Compiler

Compiled 3099 to 1902 computations (38.6% saved)

regimes326.0ms (7.8%)

Compiler: Compiled 1553 to 1198 computations (22.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

end0.0ms (0%)

sample1.2s (29%)

Algorithm

1×

intervals

Results

357.0ms	8000×	body	128	valid
7.0ms	173×	body	128	invalid

Compiler

Compiled 269 to 208 computations (22.7% saved)

Details

analyze154.0ms (3.7%)

sample20.0ms (0.5%)

simplify157.0ms (3.7%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite18.0ms (0.4%)

series106.0ms (2.5%)

simplify116.0ms (2.7%)

prune68.0ms (1.6%)

localize14.0ms (0.3%)

rewrite78.0ms (1.9%)

series188.0ms (4.5%)

simplify88.0ms (2.1%)

prune225.0ms (5.3%)

localize15.0ms (0.4%)

rewrite69.0ms (1.6%)

series220.0ms (5.2%)

simplify177.0ms (4.2%)

prune249.0ms (5.9%)

localize19.0ms (0.5%)

rewrite107.0ms (2.5%)

series170.0ms (4%)

simplify125.0ms (3%)

prune266.0ms (6.3%)

regimes326.0ms (7.8%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (29%)

Profiling