Details

analyze274.0ms (5.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample71.0ms (1.4%)

Algorithm

1×

intervals

Results

34.0ms	84×	body	1024	valid
13.0ms	37×	body	2048	valid
11.0ms	51×	body	512	valid
3.0ms	68×	body	128	valid
2.0ms	3×	body	4096	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify171.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

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: 54.5b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.9b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.0b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
13.0b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_3110`
6×	`add-sqr-sqrt_binary64_3131`
5×	`add-cube-cbrt_binary64_3142` `pow1_binary64_3168` `add-log-exp_binary64_3146`
4×	`add-exp-log_binary64_3145` `log-prod_binary64_3193`
3×	`sqrt-prod_binary64_3125` `flip3-+_binary64_3113` `add-cbrt-cube_binary64_3143` `flip-+_binary64_3084`
2×	`distribute-lft-out_binary64_3063` `sqrt-div_binary64_3126` `log-div_binary64_3194`
1×	`+-commutative_binary64_3042` `rem-sqrt-square_binary64_3123` `sqrt-pow1_binary64_3127` `sum-log_binary64_3198` `log-pow_binary64_3196` `pow1/2_binary64_3187` `rem-log-exp_binary64_3148`

Counts

3 → 42

Calls

3 calls:

7.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series187.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

87.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
63.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
37.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify100.0ms (2%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5385	862

prune81.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Merged error: 0b

Counts

52 → 4

Compiler

Compiled 819 to 542 computations (33.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
0.0b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
15.6b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_3131`
15×	`associate-l_binary64_3053`
14×	`add-exp-log_binary64_3145`
11×	`add-cube-cbrt_binary64_3142` `*-un-lft-identity_binary64_3110` `add-log-exp_binary64_3146`
10×	`associate-r_binary64_3052`
8×	`add-cbrt-cube_binary64_3143` `unpow-prod-down_binary64_3186`
7×	`unswap-sqr_binary64_3078`
6×	`prod-exp_binary64_3156`
4×	`pow1_binary64_3168` `cube-prod_binary64_3135` `sqr-pow_binary64_3082`
2×	`cbrt-unprod_binary64_3140` `pow-exp_binary64_3175` `sum-log_binary64_3198` `diff-log_binary64_3199` `*-commutative_binary64_3043` `pow-to-exp_binary64_3176`
1×	`sub-neg_binary64_3103` `+-commutative_binary64_3042` `associate--l+_binary64_3049` `flip3-+_binary64_3113` `flip3--_binary64_3114` `unpow3_binary64_3173` `flip-+_binary64_3084` `flip--_binary64_3085` `cube-mult_binary64_3137`

Counts

4 → 80

Calls

4 calls:

9.0ms	(*.f64 3/40 (pow.f64 x 5))
7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
7.0ms	(*.f64 (pow.f64 x 3) 1/6)
3.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))

series356.0ms (7%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(+.f64 x (*.f64 3/40 (pow.f64 x 5)))
65.0ms	(*.f64 3/40 (pow.f64 x 5))
60.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
50.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4967	1201
1	4967	1201

prune102.0ms (2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	92	4	96

Merged error: 0b

Counts

96 → 4

Compiler

Compiled 1698 to 1314 computations (22.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/16 (pow.f64 x 5))
0.1b	(/.f64 1/8 (pow.f64 x 3))
15.3b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
22.5b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite131.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64_3131`
71×	`times-frac_binary64_3116`
68×	`*-un-lft-identity_binary64_3110`
46×	`add-cube-cbrt_binary64_3142`
26×	`unpow-prod-down_binary64_3186`
19×	`associate-/r*_binary64_3056`
15×	`add-exp-log_binary64_3145`
14×	`cube-prod_binary64_3135`
11×	`log-prod_binary64_3193`
10×	`difference-of-squares_binary64_3079` `sqr-pow_binary64_3082`
9×	`add-log-exp_binary64_3146`
8×	`add-cbrt-cube_binary64_3143`
6×	`div-exp_binary64_3158` `distribute-lft-out--_binary64_3064` `associate-/l*_binary64_3057` `frac-sub_binary64_3119`
5×	`pow1_binary64_3168` `log-div_binary64_3194`
4×	`distribute-lft-out_binary64_3063` `unpow3_binary64_3173` `cube-mult_binary64_3137`
2×	`frac-add_binary64_3118` `cbrt-undiv_binary64_3141` `clear-num_binary64_3109` `pow-exp_binary64_3175` `flip3-+_binary64_3113` `diff-log_binary64_3199` `frac-2neg_binary64_3121` `flip3--_binary64_3114` `flip-+_binary64_3084` `div-inv_binary64_3107` `flip--_binary64_3085` `pow-to-exp_binary64_3176`
1×	`sub-neg_binary64_3103` `associate--r+_binary64_3048` `sum-log_binary64_3198` `log-pow_binary64_3196` `rem-log-exp_binary64_3148`

Counts

4 → 159

Calls

4 calls:

51.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
43.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
7.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series243.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
64.0ms	(/.f64 1/16 (pow.f64 x 5))
52.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
47.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4929	3605
1	4929	3605

prune280.0ms (5.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	171	4	175

Merged error: 0b

Counts

175 → 4

Compiler

Compiled 4100 to 3259 computations (20.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.1b	(/.f64 1/8 (pow.f64 x 3))
12.6b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite83.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64_3110`
43×	`add-sqr-sqrt_binary64_3131`
40×	`times-frac_binary64_3116`
30×	`add-cube-cbrt_binary64_3142`
13×	`cube-prod_binary64_3135` `unpow-prod-down_binary64_3186`
12×	`associate-/r*_binary64_3056`
11×	`add-log-exp_binary64_3146`
10×	`add-exp-log_binary64_3145`
6×	`distribute-lft-out_binary64_3063` `log-prod_binary64_3193` `add-cbrt-cube_binary64_3143`
5×	`pow1_binary64_3168` `difference-of-squares_binary64_3079` `sqr-pow_binary64_3082`
4×	`distribute-lft-out--_binary64_3064` `unpow3_binary64_3173` `cube-mult_binary64_3137`
3×	`div-exp_binary64_3158` `flip3-+_binary64_3113` `flip-+_binary64_3084` `associate-/l*_binary64_3057`
2×	`sum-log_binary64_3198` `diff-log_binary64_3199` `frac-sub_binary64_3119` `log-div_binary64_3194`
1×	`sub-neg_binary64_3103` `+-commutative_binary64_3042` `cbrt-undiv_binary64_3141` `clear-num_binary64_3109` `associate--l+_binary64_3049` `pow-exp_binary64_3175` `log-pow_binary64_3196` `frac-2neg_binary64_3121` `flip3--_binary64_3114` `rem-log-exp_binary64_3148` `div-inv_binary64_3107` `flip--_binary64_3085` `pow-to-exp_binary64_3176`

Counts

4 → 116

Calls

4 calls:

29.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
25.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
7.0ms	(+.f64 x (/.f64 1/2 x))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series225.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

73.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
61.0ms	(+.f64 x (/.f64 1/2 x))
46.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
44.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify82.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4907	2282
1	4907	2282

prune149.0ms (2.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	128	4	132

Merged error: 0b

Counts

132 → 4

Compiler

Compiled 2619 to 1865 computations (28.8% saved)

regimes26.0ms (0.5%)

Compiler: Compiled 63 to 51 computations (19% saved)

bsearch44.0ms (0.9%)

Steps

Iters	Range		Point
9	2.9151336866362254e-05	10.318058398541751	0.9487425125883618
10	-361.8655872889666	-8.334418280474293e-08	-1.0501776164595649

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.2s (43.8%)

Algorithm

1×

intervals

Results

954.0ms	2465×	body	1024	valid
433.0ms	1269×	body	2048	valid
278.0ms	1310×	body	512	valid
110.0ms	2289×	body	128	valid
75.0ms	619×	body	256	valid
23.0ms	48×	body	4096	valid

Compiler

Compiled 146 to 115 computations (21.2% saved)

Details

analyze274.0ms (5.4%)

sample71.0ms (1.4%)

simplify171.0ms (3.4%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite23.0ms (0.5%)

series187.0ms (3.7%)

simplify100.0ms (2%)

prune81.0ms (1.6%)

localize10.0ms (0.2%)

rewrite34.0ms (0.7%)

series356.0ms (7%)

simplify68.0ms (1.3%)

prune102.0ms (2%)

localize13.0ms (0.3%)

rewrite131.0ms (2.6%)

series243.0ms (4.8%)

simplify68.0ms (1.3%)

prune280.0ms (5.5%)

localize10.0ms (0.2%)

rewrite83.0ms (1.7%)

series225.0ms (4.5%)

simplify82.0ms (1.6%)

prune149.0ms (2.9%)

regimes26.0ms (0.5%)

bsearch44.0ms (0.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (43.8%)

Profiling