Details

analyze39.0ms (1.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

Compiler

Compiled 18 to 11 computations (38.9% saved)

sample20.0ms (0.8%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true
0.0ms	4×	pre	128	false

Compiler

Compiled 31 to 21 computations (32.3% saved)

simplify275.0ms (10.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4853	17
1	4853	17

prune5.0ms (0.2%)

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: 13.6b

Counts

2 → 2

Compiler

Compiled 59 to 43 computations (27.1% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
13.1b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite13.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
6×	`add-sqr-sqrt_binary64_789`
5×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
4×	`times-frac_binary64_773` `associate-/l*_binary64_712`
3×	`pow1_binary64_828` `sqrt-prod_binary64_783`
2×	`associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `add-log-exp_binary64_806` `div-exp_binary64_818` `difference-of-squares_binary64_736`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `associate-/r*_binary64_711` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `pow1/2_binary64_847` `flip--_binary64_742` `sqrt-pow1_binary64_785` `div-sub_binary64_772` `clear-num_binary64_766` `div-inv_binary64_764` `flip3--_binary64_771`

Counts

2 → 39

Calls

2 calls:

8.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

series131.0ms (4.8%)

Counts

2 → 6

Calls

2 calls:

68.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))
63.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))

simplify58.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4977	787
1	4977	787

prune70.0ms (2.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	43	4	47

Merged error: 0b

Counts

47 → 4

Compiler

Compiled 1244 to 573 computations (53.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
0.0b	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))
0.1b	(*.f64 b (/.f64 b a))

rewrite39.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`times-frac_binary64_773`
71×	`add-sqr-sqrt_binary64_789`
65×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
22×	`add-exp-log_binary64_805`
18×	`associate-/r*_binary64_711`
16×	`add-cbrt-cube_binary64_803`
13×	`associate-r_binary64_707`
11×	`associate-/r/_binary64_713`
9×	`div-exp_binary64_818`
8×	`pow1_binary64_828`
7×	`div-inv_binary64_764`
6×	`associate-/l*_binary64_712`
5×	`cbrt-undiv_binary64_801` `flip--_binary64_742` `flip3--_binary64_771`
4×	`add-log-exp_binary64_806`
3×	`associate-l_binary64_708` `sqrt-prod_binary64_783`
2×	`frac-2neg_binary64_778` `unswap-sqr_binary64_735` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `1-exp_binary64_811` `rec-exp_binary64_817` `clear-num_binary64_766`
1×	`rem-sqrt-square_binary64_780` `pow-flip_binary64_841` `-commutative_binary64_698` `pow1/2_binary64_847` `associate-r/_binary64_709` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `inv-pow_binary64_852`

Counts

4 → 158

Calls

4 calls:

9.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
8.0ms	(*.f64 b (/.f64 b a))
5.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))

series224.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(/.f64 a (-.f64 a (*.f64 b (/.f64 b a))))
66.0ms	(/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))
60.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (*.f64 b (/.f64 b a)))))))
29.0ms	(*.f64 b (/.f64 b a))

simplify96.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5726	3547

prune152.0ms (5.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	169	5	174

Merged error: 0b

Counts

174 → 5

Compiler

Compiled 3638 to 1284 computations (64.7% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
0.1b	(*.f64 b (/.f64 b a))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_789`
20×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
19×	`times-frac_binary64_773`
13×	`associate-r_binary64_707`
10×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
6×	`pow1_binary64_828`
3×	`associate-l_binary64_708` `associate-/r_binary64_711` `add-log-exp_binary64_806` `associate-/l_binary64_712` `sqrt-prod_binary64_783`
2×	`unswap-sqr_binary64_735` `associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `div-exp_binary64_818` `div-inv_binary64_764`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `-commutative_binary64_698` `pow1/2_binary64_847` `associate-r/_binary64_709` `flip--_binary64_742` `sqrt-pow1_binary64_785` `div-sub_binary64_772` `pow-prod-down_binary64_838` `clear-num_binary64_766` `flip3--_binary64_771`

Counts

3 → 75

Calls

3 calls:

8.0ms	(*.f64 b (/.f64 b a))
6.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))

series163.0ms (6%)

Counts

3 → 9

Calls

3 calls:

75.0ms	(/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)
59.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 a (*.f64 b (/.f64 b a))) a)))
29.0ms	(*.f64 b (/.f64 b a))

simplify57.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4954	1284
1	4954	1284

prune64.0ms (2.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	84	5	89

Merged error: 0b

Counts

89 → 5

Compiler

Compiled 1457 to 505 computations (65.3% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
0.4b	(*.f64 (/.f64 b a) (/.f64 b a))

rewrite24.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_789`
40×	`times-frac_binary64_773`
31×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
14×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
13×	`associate-l_binary64_708` `associate-r_binary64_707` `swap-sqr_binary64_734`
10×	`pow1_binary64_828`
4×	`unswap-sqr_binary64_735` `cbrt-undiv_binary64_801` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `div-exp_binary64_818` `div-inv_binary64_764`
3×	`sqrt-prod_binary64_783`
2×	`add-log-exp_binary64_806`
1×	`pow2_binary64_848` `frac-times_binary64_777` `rem-sqrt-square_binary64_780` `pow-prod-up_binary64_837` `pow-plus_binary64_830` `-commutative_binary64_698` `pow1/2_binary64_847` `associate-r/_binary64_709` `associate-*l/_binary64_710` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `pow-sqr_binary64_740`

Counts

2 → 80

Calls

2 calls:

14.0ms	(*.f64 (/.f64 b a) (/.f64 b a))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))

series84.0ms (3.1%)

Counts

2 → 6

Calls

2 calls:

48.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
36.0ms	(*.f64 (/.f64 b a) (/.f64 b a))

simplify78.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4924	966
1	4924	966

prune91.0ms (3.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	2	0	2
Picked	1	0	1
Done	1	1	2
Total	87	4	91

Merged error: 0b

Counts

91 → 4

Compiler

Compiled 1432 to 835 computations (41.7% saved)

regimes161.0ms (6%)

Compiler: Compiled 1533 to 1050 computations (31.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	14
1	20	14

end0.0ms (0%)

sample798.0ms (29.6%)

Algorithm

1×

intervals

Results

269.0ms	8000×	body	128	valid
150.0ms	8000×	pre	128	true
3.0ms	132×	pre	128	false

Compiler

Compiled 213 to 150 computations (29.6% saved)

Details

analyze39.0ms (1.4%)

sample20.0ms (0.8%)

simplify275.0ms (10.2%)

prune5.0ms (0.2%)

localize7.0ms (0.3%)

rewrite13.0ms (0.5%)

series131.0ms (4.8%)

simplify58.0ms (2.1%)

prune70.0ms (2.6%)

localize9.0ms (0.3%)

rewrite39.0ms (1.5%)

series224.0ms (8.3%)

simplify96.0ms (3.6%)

prune152.0ms (5.6%)

localize8.0ms (0.3%)

rewrite21.0ms (0.8%)

series163.0ms (6%)

simplify57.0ms (2.1%)

prune64.0ms (2.4%)

localize6.0ms (0.2%)

rewrite24.0ms (0.9%)

series84.0ms (3.1%)

simplify78.0ms (2.9%)

prune91.0ms (3.4%)

regimes161.0ms (6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample798.0ms (29.6%)

Profiling