Details

Time bar (total: 14.8s)

analyze2.0s (13.3%)

Algorithm
1×search
Search
TrueOtherFalseIter
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
0%99.9%0.1%5
0%99.9%0.1%6
0%99.9%0.1%7
1.6%98.3%0.1%8
2.3%97.5%0.1%9
7.4%90.9%1.7%10
9.2%87.4%3.5%11
11.7%83.5%4.8%12
15.2%76%8.8%13
16.4%72%11.6%14
Compiler

Compiled 26 to 22 computations (15.4% saved)

sample101.0ms (0.7%)

Algorithm
1×intervals
Results
45.0ms92×body1024valid
15.0ms119×body128valid
14.0ms29×body512valid
6.0ms50×body128invalid
4.0ms16×body256valid
2.0ms7×body256invalid
2.0ms6×body512invalid
0.0ms1×body1024invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify144.0ms (1%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
0493135
1493135

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 33.9b

Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
3.2b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
12.9b
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
20.9b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite68.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64_116
58×prod-exp_binary64_127
52×add-cbrt-cube_binary64_114
28×times-frac_binary64_84
26×add-sqr-sqrt_binary64_100 cbrt-unprod_binary64_111
24×div-exp_binary64_129
20×pow1_binary64_139
19×*-un-lft-identity_binary64_78
18×associate-*l*_binary64_19
17×add-cube-cbrt_binary64_113
16×associate-*l/_binary64_21
12×associate-/l*_binary64_23
10×unpow-prod-down_binary64_157 frac-times_binary64_88 associate-*r*_binary64_18 pow-prod-down_binary64_149 cube-prod_binary64_106
8×tan-quot_binary64_237 pow-exp_binary64_146 pow-to-exp_binary64_147 cbrt-undiv_binary64_112
6×associate-*r/_binary64_20
5×unswap-sqr_binary64_46
4×add-log-exp_binary64_117 flip-+_binary64_52 sqr-pow_binary64_50 flip3-+_binary64_81
3×cube-mult_binary64_108 *-commutative_binary64_9 unpow3_binary64_144
2×div-inv_binary64_75
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 frac-2neg_binary64_89 associate-/r*_binary64_22 clear-num_binary64_77 distribute-lft-out_binary64_29
Counts
4 → 159
Calls

4 calls:

22.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
12.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
10.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
7.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

series661.0ms (4.5%)

Counts
4 → 12
Calls

4 calls:

382.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
180.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
68.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
31.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify69.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
171 → 171
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
055553677

prune268.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New16011171
Fresh000
Picked101
Done000
Total16111172

Merged error: 16.3b

Counts
172 → 11
Compiler

Compiled 5076 to 2799 computations (44.9% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.5b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
4.1b
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
9.9b
(/.f64 (*.f64 t t) l)
12.9b
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite74.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
113×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
65×cbrt-unprod_binary64_111 prod-exp_binary64_127
44×associate-*l/_binary64_21
34×frac-times_binary64_88
29×pow1_binary64_139
20×cbrt-undiv_binary64_112 div-exp_binary64_129
17×pow-prod-down_binary64_149
16×tan-quot_binary64_237
15×add-sqr-sqrt_binary64_100
14×associate-*r/_binary64_20
13×*-un-lft-identity_binary64_78
11×add-cube-cbrt_binary64_113
10×associate-*r*_binary64_18
9×associate-*l*_binary64_19
8×flip-+_binary64_52 flip3-+_binary64_81
7×times-frac_binary64_84
4×add-log-exp_binary64_117
3×*-commutative_binary64_9 associate-/r*_binary64_22
2×div-inv_binary64_75 unswap-sqr_binary64_46
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 frac-2neg_binary64_89 associate-/l*_binary64_23 clear-num_binary64_77 distribute-lft-out_binary64_29
Counts
4 → 151
Calls

4 calls:

26.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
14.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
7.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
5.0ms
(/.f64 (*.f64 t t) l)

series630.0ms (4.3%)

Counts
4 → 12
Calls

4 calls:

381.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
182.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
55.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
13.0ms
(/.f64 (*.f64 t t) l)

simplify87.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049674012
149674012

prune230.0ms (1.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New1558163
Fresh4610
Picked101
Done000
Total16014174

Merged error: 10.5b

Counts
174 → 14
Compiler

Compiled 5096 to 2578 computations (49.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
2.5b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
2.7b
(*.f64 (/.f64 t l) (sin.f64 k))
12.9b
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite153.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
421×add-exp-log_binary64_116
304×add-cbrt-cube_binary64_114
259×prod-exp_binary64_127
181×cbrt-unprod_binary64_111
179×frac-times_binary64_88
178×associate-*l/_binary64_21
108×div-exp_binary64_129
81×associate-*r/_binary64_20
69×cbrt-undiv_binary64_112
56×tan-quot_binary64_237
47×associate-/r/_binary64_24
40×pow1_binary64_139
32×flip-+_binary64_52 flip3-+_binary64_81
26×pow-prod-down_binary64_149
21×add-sqr-sqrt_binary64_100
18×1-exp_binary64_122 *-un-lft-identity_binary64_78
16×add-cube-cbrt_binary64_113
15×associate-*l*_binary64_19
13×times-frac_binary64_84
10×associate-*r*_binary64_18
4×add-log-exp_binary64_117
3×*-commutative_binary64_9 associate-/l*_binary64_23
2×div-inv_binary64_75 unswap-sqr_binary64_46
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 frac-2neg_binary64_89 associate-/r*_binary64_22 clear-num_binary64_77 distribute-lft-out_binary64_29
Counts
4 → 308
Calls

4 calls:

35.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
34.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
18.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series925.0ms (6.3%)

Counts
4 → 12
Calls

4 calls:

395.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
298.0ms
(/.f64 2 (*.f64 (*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2))))
178.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
54.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify157.0ms (1.1%)

Algorithm
1×egg-herbie
Counts
320 → 320
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
049629870
149629870

prune544.0ms (3.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New31010320
Fresh8513
Picked101
Done000
Total31915334

Merged error: 7.7b

Counts
334 → 15
Compiler

Compiled 9954 to 5298 computations (46.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
2.5b
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
2.7b
(*.f64 (/.f64 t l) (sin.f64 k))
12.9b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite82.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
125×add-cbrt-cube_binary64_114 add-exp-log_binary64_116
78×cbrt-unprod_binary64_111 prod-exp_binary64_127
49×pow1_binary64_139
41×associate-*r/_binary64_20
39×associate-*l/_binary64_21
35×frac-times_binary64_88
32×pow-prod-down_binary64_149
28×associate-*l*_binary64_19
26×add-sqr-sqrt_binary64_100
23×*-un-lft-identity_binary64_78
21×add-cube-cbrt_binary64_113
19×times-frac_binary64_84
18×tan-quot_binary64_237
16×cbrt-undiv_binary64_112 div-exp_binary64_129
11×associate-*r*_binary64_18
8×flip-+_binary64_52 flip3-+_binary64_81
4×*-commutative_binary64_9 add-log-exp_binary64_117
2×div-inv_binary64_75 unswap-sqr_binary64_46
1×distribute-lft-in_binary64_27 distribute-rgt-in_binary64_28 distribute-lft-out_binary64_29
Counts
4 → 176
Calls

4 calls:

26.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
15.0ms
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
11.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
7.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series803.0ms (5.4%)

Counts
4 → 12
Calls

4 calls:

391.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
181.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
174.0ms
(*.f64 (/.f64 t l) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
57.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify94.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
188 → 188
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
049815129
149815129

prune215.0ms (1.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New1835188
Fresh11314
Picked101
Done000
Total18518203

Merged error: 7.5b

Counts
203 → 18
Compiler

Compiled 5720 to 2045 computations (64.2% saved)

regimes1.6s (10.7%)

Compiler

Compiled 19750 to 14648 computations (25.8% saved)

bsearch154.0ms (1%)

Steps
ItersRangePoint
9
3.249180317868675e-171
8.452977006830115e-165
2.4546753454364185e-165
6
-2.3471768353313476e-193
-3.344043374453203e-194
-2.2983692557782696e-193
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04389
14389

end0.0ms (0%)

sample5.7s (38.6%)

Algorithm
1×intervals
Results
1.3s2697×body1024valid
458.0ms1248×body512valid
429.0ms3469×body128valid
168.0ms1391×body128invalid
144.0ms577×body256valid
50.0ms139×body512invalid
31.0ms61×body1024invalid
27.0ms101×body256invalid
7.0ms9×body2048valid
Compiler

Compiled 3200 to 2363 computations (26.2% saved)

Profiling

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