Details

analyze257.0ms (5.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample56.0ms (1.1%)

Algorithm

1×

intervals

Results

30.0ms	68×	body	2048	valid
7.0ms	30×	body	1024	valid
6.0ms	46×	body	512	valid
4.0ms	90×	body	128	valid
2.0ms	20×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify174.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	364	12
1	364	12

prune2.0ms (0%)

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: 29.5b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(-.f64 1 (cos.f64 x))
16.3b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
7×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
6×	`times-frac_binary64_83` `associate-/l*_binary64_24` `difference-of-squares_binary64_46`
4×	`add-log-exp_binary64_113` `add-cube-cbrt_binary64_109`
3×	`distribute-lft-out--_binary64_31`
2×	`cbrt-undiv_binary64_108` `pow1_binary64_135` `flip--_binary64_52` `div-exp_binary64_125` `flip3--_binary64_81` `associate-/l/_binary64_26`
1×	`associate-/r*_binary64_23` `cbrt-unprod_binary64_107` `div-sub_binary64_82` `sub-neg_binary64_70` `prod-exp_binary64_123` `clear-num_binary64_76` `diff-log_binary64_166` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

2 → 44

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

series80.0ms (1.6%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
23.0ms	(-.f64 1 (cos.f64 x))

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5002	700

prune63.0ms (1.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Merged error: 0.0b

Counts

51 → 7

Compiler

Compiled 744 to 407 computations (45.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.5b	(+.f64 1 (cos.f64 x))
16.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
24×	`*-un-lft-identity_binary64_77`
22×	`times-frac_binary64_83`
16×	`add-sqr-sqrt_binary64_98`
14×	`add-cube-cbrt_binary64_109`
12×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
11×	`pow1_binary64_135` `associate-/l*_binary64_24`
7×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
6×	`add-log-exp_binary64_113` `associate-/r/_binary64_25`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_51` `flip3-+_binary64_80` `div-inv_binary64_74`
3×	`associate-l_binary64_20` `div-sub_binary64_82` `sqr-sin-a_binary64_222` `swap-sqr_binary64_44` `associate-r_binary64_19`
2×	`sin-mult_binary64_229` `clear-num_binary64_76` `associate-/l/_binary64_26` `frac-2neg_binary64_88`
1×	`pow2_binary64_155` `pow-prod-down_binary64_145` `pow-sqr_binary64_50` `pow-plus_binary64_137` `pow-prod-up_binary64_144` `+-commutative_binary64_9` `unswap-sqr_binary64_45` `*-commutative_binary64_10` `sum-log_binary64_165`

Counts

4 → 111

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
9.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series259.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
89.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
26.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
12.0ms	(+.f64 1 (cos.f64 x))

simplify65.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4970	1781
1	4970	1781

prune112.0ms (2.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	124	6	130

Merged error: 0b

Counts

130 → 6

Compiler

Compiled 2148 to 1081 computations (49.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))
0.5b	(+.f64 1 (cos.f64 x))
0.5b	(+.f64 1 (cos.f64 x))
0.6b	(*.f64 (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x) (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x))

rewrite253.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Rules

781×	`times-frac_binary64_83`
486×	`*-un-lft-identity_binary64_77`
456×	`add-sqr-sqrt_binary64_98`
348×	`add-cube-cbrt_binary64_109`
222×	`sqrt-prod_binary64_92`
121×	`swap-sqr_binary64_44`
85×	`associate-l_binary64_20` `associate-r_binary64_19`
60×	`distribute-lft-out_binary64_30`
42×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
26×	`sqrt-div_binary64_93` `associate-/r/_binary64_25`
19×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
17×	`div-inv_binary64_74`
16×	`unswap-sqr_binary64_45`
15×	`flip-+_binary64_51` `flip3-+_binary64_80`
11×	`pow1_binary64_135`
9×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
8×	`add-log-exp_binary64_113`
7×	`associate-/r*_binary64_23`
3×	`associate-/l*_binary64_24`
2×	`+-commutative_binary64_9` `sum-log_binary64_165`
1×	`pow2_binary64_155` `pow-prod-down_binary64_145` `pow-sqr_binary64_50` `pow-plus_binary64_137` `frac-times_binary64_87` `pow-prod-up_binary64_144` `associate-l/_binary64_22` `associate-r/_binary64_21` `*-commutative_binary64_10` `clear-num_binary64_76` `frac-2neg_binary64_88`

Counts

4 → 410

Calls

4 calls:

137.0ms	(*.f64 (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x) (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x))
8.0ms	(/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))
4.0ms	(+.f64 1 (cos.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series271.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(*.f64 (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x) (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x))
119.0ms	(/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))
10.0ms	(+.f64 1 (cos.f64 x))
10.0ms	(+.f64 1 (cos.f64 x))

simplify199.0ms (4%)

Algorithm

1×	egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5013	18142

prune780.0ms (15.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	422	0	422
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	422	6	428

Merged error: 0b

Counts

428 → 6

Compiler

Compiled 14925 to 7394 computations (50.5% saved)

localize15.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.2b	(*.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x)))
16.5b	(/.f64 (.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x))) (neg.f64 (.f64 x x)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_98` `associate-r_binary64_19`
9×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
8×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
6×	`associate-/r*_binary64_23` `times-frac_binary64_83`
5×	`distribute-lft-neg-in_binary64_36` `distribute-rgt-neg-in_binary64_37`
4×	`pow1_binary64_135`
3×	`associate-l_binary64_20` `neg-mul-1_binary64_73`
2×	`add-log-exp_binary64_113` `cbrt-unprod_binary64_107` `cbrt-undiv_binary64_108` `tan-quot_binary64_233` `associate-*l/_binary64_22` `div-exp_binary64_125` `prod-exp_binary64_123` `distribute-rgt-neg-out_binary64_39`
1×	`pow-prod-down_binary64_145` `associate-/l_binary64_24` `unswap-sqr_binary64_45` `-commutative_binary64_10` `distribute-frac-neg_binary64_42` `clear-num_binary64_76` `associate-/l/_binary64_26` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

2 → 56

Calls

2 calls:

9.0ms	(/.f64 (.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x))) (neg.f64 (.f64 x x)))
8.0ms	(*.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x)))

series253.0ms (5.1%)

Counts

2 → 6

Calls

2 calls:

137.0ms	(/.f64 (.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x))) (neg.f64 (.f64 x x)))
116.0ms	(*.f64 (tan.f64 (/.f64 x 2)) (neg.f64 (sin.f64 x)))

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4927	1105
1	4927	1105

prune50.0ms (1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	62	6	68

Merged error: 0b

Counts

68 → 6

Compiler

Compiled 1044 to 496 computations (52.5% saved)

regimes14.0ms (0.3%)

Compiler: Compiled 88 to 65 computations (26.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	34
1	12	34

end0.0ms (0%)

sample1.8s (36.9%)

Algorithm

1×

intervals

Results

851.0ms	1928×	body	2048	valid
237.0ms	1093×	body	1024	valid
222.0ms	1479×	body	512	valid
111.0ms	2651×	body	128	valid
79.0ms	749×	body	256	valid
43.0ms	100×	body	4096	valid

Compiler

Compiled 116 to 85 computations (26.7% saved)

Details

analyze257.0ms (5.2%)

sample56.0ms (1.1%)

simplify174.0ms (3.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite16.0ms (0.3%)

series80.0ms (1.6%)

simplify55.0ms (1.1%)

prune63.0ms (1.3%)

localize11.0ms (0.2%)

rewrite42.0ms (0.8%)

series259.0ms (5.2%)

simplify65.0ms (1.3%)

prune112.0ms (2.3%)

localize11.0ms (0.2%)

rewrite253.0ms (5.1%)

series271.0ms (5.5%)

simplify199.0ms (4%)

prune780.0ms (15.7%)

localize15.0ms (0.3%)

rewrite22.0ms (0.4%)

series253.0ms (5.1%)

simplify68.0ms (1.4%)

prune50.0ms (1%)

regimes14.0ms (0.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (36.9%)

Profiling