Details

analyze5.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample18.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify275.0ms (8.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	5574	20

prune2.0ms (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: 0.0b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.0b	(-.f64 1 (*.f64 x x))
0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite67.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64_767`
26×	`times-frac_binary64_773`
23×	`add-sqr-sqrt_binary64_789`
16×	`distribute-lft-out_binary64_718`
15×	`log-prod_binary64_853`
14×	`add-cube-cbrt_binary64_802`
12×	`div-inv_binary64_764`
11×	`sqrt-prod_binary64_783`
8×	`add-log-exp_binary64_806`
6×	`pow1_binary64_828` `distribute-rgt-out_binary64_720`
5×	`add-exp-log_binary64_805`
4×	`add-cbrt-cube_binary64_803` `difference-of-squares_binary64_736`
3×	`log-div_binary64_854`
2×	`frac-add_binary64_775` `flip-+_binary64_741` `distribute-rgt1-in_binary64_723` `flip3-+_binary64_770` `flip--_binary64_742` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `sub-neg_binary64_760` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `log-pow_binary64_856` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `rem-log-exp_binary64_808` `sqrt-pow1_binary64_785`

Counts

4 → 82

Calls

4 calls:

28.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
24.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
4.0ms	(-.f64 1 (*.f64 x x))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series247.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
56.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
51.0ms	(-.f64 1 (*.f64 x x))
41.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify100.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4885	1861
1	4885	1861

prune102.0ms (3.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	92	3	95

Merged error: 0.0b

Counts

95 → 3

Compiler

Compiled 1913 to 1266 computations (33.8% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (*.f64 x x))
0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.6b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3))
0.7b	(pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3)

rewrite44.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_767`
19×	`add-sqr-sqrt_binary64_789`
15×	`log-prod_binary64_853` `add-cube-cbrt_binary64_802`
14×	`cbrt-prod_binary64_798`
13×	`times-frac_binary64_773`
10×	`pow1_binary64_828`
8×	`distribute-lft-out_binary64_718` `cube-prod_binary64_795` `unpow-prod-down_binary64_846`
6×	`add-exp-log_binary64_805` `add-log-exp_binary64_806` `div-inv_binary64_764`
5×	`log-pow_binary64_856` `add-cbrt-cube_binary64_803`
3×	`log-div_binary64_854` `pow-unpow_binary64_844` `sqrt-prod_binary64_783` `distribute-rgt-out_binary64_720`
2×	`sqr-pow_binary64_739` `cube-mult_binary64_797` `unpow3_binary64_833` `difference-of-squares_binary64_736`
1×	`pow-to-exp_binary64_836` `pow1/3_binary64_849` `pow-exp_binary64_835` `frac-add_binary64_775` `sub-neg_binary64_760` `flip-+_binary64_741` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `rem-cbrt-cube_binary64_791` `rem-cube-cbrt_binary64_790` `rem-log-exp_binary64_808` `distribute-rgt1-in_binary64_723` `flip3-+_binary64_770` `flip--_binary64_742` `flip3--_binary64_771` `pow-pow_binary64_839`

Counts

4 → 89

Calls

4 calls:

27.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
4.0ms	(-.f64 1 (*.f64 x x))
3.0ms	(pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3)
3.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3))

series389.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3)
96.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
91.0ms	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 3))
54.0ms	(-.f64 1 (*.f64 x x))

simplify70.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5086	2647

prune132.0ms (4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	100	4	104

Merged error: 0.0b

Counts

104 → 4

Compiler

Compiled 2432 to 1709 computations (29.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 1 (*.f64 x x))
0.0b	(log.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))))
0.4b	(-.f64 (log.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))))) (log.f64 (*.f64 x x)))
31.1b	(log.f64 (*.f64 x x))

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`pow1_binary64_828`
20×	`log-pow_binary64_856`
13×	`*-un-lft-identity_binary64_767`
10×	`add-sqr-sqrt_binary64_789` `cancel-sign-sub-inv_binary64_733`
8×	`add-exp-log_binary64_805` `log-prod_binary64_853`
7×	`add-cube-cbrt_binary64_802`
6×	`add-log-exp_binary64_806` `distribute-lft-out--_binary64_719`
4×	`log-div_binary64_854` `pow-prod-down_binary64_838` `add-cbrt-cube_binary64_803`
3×	`rem-log-exp_binary64_808` `difference-of-squares_binary64_736` `associate--l+_binary64_704`
2×	`pow2_binary64_848` `pow-prod-up_binary64_837` `pow-plus_binary64_830` `sub-neg_binary64_760` `flip-+_binary64_741` `diff-log_binary64_859` `flip3-+_binary64_770` `flip--_binary64_742` `pow-sqr_binary64_740` `flip3--_binary64_771` `associate--l-_binary64_705`
1×	`prod-exp_binary64_816` `associate--r+_binary64_703`

Counts

4 → 77

Calls

4 calls:

10.0ms	(-.f64 (log.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))))) (log.f64 (*.f64 x x)))
4.0ms	(-.f64 1 (*.f64 x x))
3.0ms	(log.f64 (*.f64 x x))
3.0ms	(log.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))))

series362.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(-.f64 (log.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))))) (log.f64 (*.f64 x x)))
97.0ms	(log.f64 (+.f64 x (.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))))
82.0ms	(log.f64 (*.f64 x x))
48.0ms	(-.f64 1 (*.f64 x x))

simplify131.0ms (4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4834	1532
1	4834	1532

prune105.0ms (3.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	1	1
Picked	0	1	1
Done	1	1	2
Total	89	4	93

Merged error: 0.0b

Counts

93 → 4

Compiler

Compiled 2129 to 1216 computations (42.9% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0b	(/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
0.0b	(-.f64 1 (*.f64 x x))
0.0b	(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))

rewrite37.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64_767`
32×	`add-sqr-sqrt_binary64_789`
30×	`times-frac_binary64_773`
23×	`add-cube-cbrt_binary64_802`
19×	`log-prod_binary64_853`
16×	`distribute-lft-out_binary64_718`
9×	`add-exp-log_binary64_805`
8×	`add-log-exp_binary64_806` `sqrt-prod_binary64_783`
6×	`add-cbrt-cube_binary64_803`
5×	`pow1_binary64_828` `associate-/l*_binary64_712`
3×	`associate-/r*_binary64_711`
2×	`associate-/l/_binary64_714` `flip-+_binary64_741` `rem-log-exp_binary64_808` `flip3-+_binary64_770` `div-exp_binary64_818` `div-inv_binary64_764` `difference-of-squares_binary64_736`
1×	`frac-2neg_binary64_778` `log-div_binary64_854` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `log-pow_binary64_856` `+-commutative_binary64_697` `sum-log_binary64_858` `flip--_binary64_742` `clear-num_binary64_766` `flip3--_binary64_771`

Counts

4 → 94

Calls

4 calls:

12.0ms	(/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
8.0ms	(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
6.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
3.0ms	(-.f64 1 (*.f64 x x))

series226.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(log.f64 (/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))
55.0ms	(/.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x)
46.0ms	(-.f64 1 (*.f64 x x))
30.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify78.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4919	2210
1	4919	2210

prune112.0ms (3.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	106	4	110

Merged error: 0.0b

Counts

110 → 4

Compiler

Compiled 1971 to 1315 computations (33.3% saved)

regimes42.0ms (1.3%)

Compiler: Compiled 238 to 175 computations (26.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	17
1	28	17

end0.0ms (0%)

sample643.0ms (19.7%)

Algorithm

1×

intervals

Results

428.0ms	8000×	body	128	valid
0.0ms	6×	body	128	nan

Compiler

Compiled 87 to 66 computations (24.1% saved)

Details

analyze5.0ms (0.1%)

sample18.0ms (0.6%)

simplify275.0ms (8.4%)

prune2.0ms (0.1%)

localize9.0ms (0.3%)

rewrite67.0ms (2%)

series247.0ms (7.6%)

simplify100.0ms (3.1%)

prune102.0ms (3.1%)

localize12.0ms (0.4%)

rewrite44.0ms (1.4%)

series389.0ms (11.9%)

simplify70.0ms (2.1%)

prune132.0ms (4%)

localize11.0ms (0.3%)

rewrite28.0ms (0.9%)

series362.0ms (11.1%)

simplify131.0ms (4%)

prune105.0ms (3.2%)

localize8.0ms (0.2%)

rewrite37.0ms (1.1%)

series226.0ms (6.9%)

simplify78.0ms (2.4%)

prune112.0ms (3.4%)

regimes42.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample643.0ms (19.7%)

Profiling