Details

Time bar (total: 29.9s)

analyze2.9s (9.8%)

Algorithm
1×search
2×egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04978140
14978140
033
133
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)

sample106.0ms (0.4%)

Algorithm
1×intervals
Results
49.0ms83×body1024valid
16.0ms122×body128valid
13.0ms34×body512valid
5.0ms17×body256valid
4.0ms36×body128invalid
2.0ms4×body512invalid
1.0ms3×body256invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify59.0ms (0.2%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
0493135
1493135

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112
Error
31.1b
Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
2.5b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
12.4b
(*.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)))
19.0b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite400.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Error
16.7b
Rules
108×add-exp-log_binary64_457
58×prod-exp_binary64_468
52×add-cbrt-cube_binary64_455
28×times-frac_binary64_425
26×cbrt-unprod_binary64_452 add-sqr-sqrt_binary64_441
24×div-exp_binary64_470
20×pow1_binary64_480
19×*-un-lft-identity_binary64_419
18×associate-*l*_binary64_360
17×add-cube-cbrt_binary64_454
16×associate-*l/_binary64_362
12×associate-/l*_binary64_364
10×unpow-prod-down_binary64_498 cube-prod_binary64_447 pow-prod-down_binary64_490 frac-times_binary64_429 associate-*r*_binary64_359
8×pow-to-exp_binary64_488 pow-exp_binary64_487 cbrt-undiv_binary64_453 tan-quot_binary64_578
6×associate-*r/_binary64_361
5×unswap-sqr_binary64_387
4×add-log-exp_binary64_458 sqr-pow_binary64_391 flip3-+_binary64_422 flip-+_binary64_393
3×unpow3_binary64_485 cube-mult_binary64_449 *-commutative_binary64_350
2×div-inv_binary64_416
1×frac-2neg_binary64_430 clear-num_binary64_418 associate-/r*_binary64_363 distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368 distribute-lft-out_binary64_370
Counts
4 → 159
Calls

4 calls:

31.0ms
(*.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))
11.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
7.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
Compiler

Compiled 5186 to 2726 computations (47.4% saved)

series2.0s (6.8%)

Error
22.9b
Counts
4 → 42
Calls

4 calls:

1.0s
(*.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)))
538.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
258.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
125.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))
Compiler

Compiled 3210 to 2529 computations (21.2% saved)

simplify115.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
051254521

prune412.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New18813201
Fresh000
Picked101
Done000
Total18913202
Error
13.4b
Counts
202 → 13
Compiler

Compiled 5899 to 3220 computations (45.4% saved)

localize40.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
2.4b
(*.f64 (sin.f64 k) (/.f64 t l))
8.3b
(/.f64 (*.f64 t t) l)
12.4b
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite374.0ms (1.3%)

Algorithm
1×rewrite-expression-head
Error
9.3b
Rules
120×add-exp-log_binary64_457 add-cbrt-cube_binary64_455
70×prod-exp_binary64_468 cbrt-unprod_binary64_452
34×frac-times_binary64_429
31×associate-*r/_binary64_361
29×pow1_binary64_480
27×associate-*l/_binary64_362
21×div-exp_binary64_470 cbrt-undiv_binary64_453 add-sqr-sqrt_binary64_441
20×associate-*r*_binary64_359
18×*-un-lft-identity_binary64_419
17×pow-prod-down_binary64_490
16×add-cube-cbrt_binary64_454 tan-quot_binary64_578
13×times-frac_binary64_425
8×flip3-+_binary64_422 flip-+_binary64_393
5×associate-*l*_binary64_360
4×add-log-exp_binary64_458
3×*-commutative_binary64_350 associate-/r*_binary64_363
2×div-inv_binary64_416 unswap-sqr_binary64_387
1×distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368 distribute-lft-out_binary64_370 frac-2neg_binary64_430 clear-num_binary64_418 associate-/l*_binary64_364
Counts
4 → 159
Calls

4 calls:

48.0ms
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
14.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
8.0ms
(*.f64 (sin.f64 k) (/.f64 t l))
5.0ms
(/.f64 (*.f64 t t) l)
Compiler

Compiled 6030 to 1992 computations (67% saved)

series2.1s (6.9%)

Error
13.3b
Counts
4 → 42
Calls

4 calls:

1.1s
(*.f64 (*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
520.0ms
(*.f64 (*.f64 (/.f64 (*.f64 t t) l) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
255.0ms
(*.f64 (sin.f64 k) (/.f64 t l))
84.0ms
(/.f64 (*.f64 t t) l)
Compiler

Compiled 3288 to 2426 computations (26.2% saved)

simplify133.0ms (0.4%)

Algorithm
1×egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 0 (78.0ms)

IterNodesCost
049574829
149574829

prune351.0ms (1.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1947201
Fresh8412
Picked101
Done000
Total20311214
Error
9.7b
Counts
214 → 11
Compiler

Compiled 5972 to 2933 computations (50.9% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.1b
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l)))
2.3b
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
2.4b
(*.f64 (sin.f64 k) (/.f64 t l))
12.4b
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite518.0ms (1.7%)

Algorithm
1×rewrite-expression-head
Error
6.8b
Rules
151×add-exp-log_binary64_457 add-cbrt-cube_binary64_455
78×prod-exp_binary64_468 cbrt-unprod_binary64_452
76×times-frac_binary64_425
54×add-sqr-sqrt_binary64_441
51×*-un-lft-identity_binary64_419
49×add-cube-cbrt_binary64_454 associate-*l*_binary64_360
37×div-exp_binary64_470 cbrt-undiv_binary64_453
35×frac-times_binary64_429
34×pow1_binary64_480 associate-*r/_binary64_361
28×associate-*l/_binary64_362
21×associate-*r*_binary64_359
20×pow-prod-down_binary64_490
16×tan-quot_binary64_578
8×flip3-+_binary64_422 flip-+_binary64_393
5×div-inv_binary64_416
4×add-log-exp_binary64_458 *-commutative_binary64_350
2×unswap-sqr_binary64_387
1×distribute-rgt-in_binary64_369 distribute-lft-in_binary64_368 distribute-lft-out_binary64_370 associate-/r/_binary64_365
Counts
4 → 214
Calls

4 calls:

37.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l)))
34.0ms
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
33.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
12.0ms
(*.f64 (sin.f64 k) (/.f64 t l))
Compiler

Compiled 8160 to 2642 computations (67.6% saved)

series2.3s (7.6%)

Error
9.7b
Counts
4 → 46
Calls

4 calls:

1.0s
(*.f64 (*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k)) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
665.0ms
(*.f64 (*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l))) (tan.f64 k))
321.0ms
(*.f64 (/.f64 t (/.f64 l t)) (*.f64 (sin.f64 k) (/.f64 t l)))
189.0ms
(*.f64 (sin.f64 k) (/.f64 t l))
Compiler

Compiled 3556 to 2673 computations (24.8% saved)

simplify143.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
260 → 260
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049726279
149726279

prune454.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New2546260
Fresh6410
Picked101
Done000
Total26110271
Error
6.8b
Counts
271 → 10
Compiler

Compiled 7919 to 3750 computations (52.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b
(/.f64 (*.f64 t (sin.f64 k)) l)
2.3b
(*.f64 (tan.f64 k) (*.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)))
5.8b
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)))) (/.f64 l t))
10.2b
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (/.f64 (*.f64 t (sin.f64 k)) l))))

rewrite331.0ms (1.1%)

Algorithm
1×rewrite-expression-head
Error
6.8b
Rules
103×add-exp-log_binary64_457 add-cbrt-cube_binary64_455
48×prod-exp_binary64_468 cbrt-unprod_binary64_452
34×times-frac_binary64_425
28×div-exp_binary64_470 cbrt-undiv_binary64_453
27×associate-*r/_binary64_361
24×*-un-lft-identity_binary64_419
22×add-cube-cbrt_binary64_454 add-sqr-sqrt_binary64_441
19×frac-times_binary64_429
18×pow1_binary64_480
16×associate-/r*_binary64_363
14×tan-quot_binary64_578
11×associate-*l/_binary64_362 associate-/l/_binary64_366
9×pow-prod-down_binary64_490
8×flip3-+_binary64_422 flip-+_binary64_393
7×associate-*l*_binary64_360
4×add-log-exp_binary64_458 div-inv_binary64_416
2×associate-*r*_binary64_359 *-commutative_binary64_350 frac-2neg_binary64_430 clear-num_binary64_418 associate-/l*_binary64_364
1×distribute-lft-out_binary64_370 associate-/r/_binary64_365
Counts
4 → 156
Calls

4 calls:

25.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)))) (/.f64 l t))
22.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (/.f64 (*.f64 t (sin.f64 k)) l))))
19.0ms
(*.f64 (tan.f64 k) (*.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)))
9.0ms
(/.f64 (*.f64 t (sin.f64 k)) l)
Compiler

Compiled 6005 to 2120 computations (64.7% saved)

series2.7s (8.9%)

Error
5.6b
Counts
4 → 54
Calls

4 calls:

990.0ms
(/.f64 (*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)))) (/.f64 l t))
905.0ms
(*.f64 (+.f64 2 (pow.f64 (/.f64 k t) 2)) (*.f64 (tan.f64 k) (*.f64 t (/.f64 (*.f64 t (sin.f64 k)) l))))
484.0ms
(*.f64 (tan.f64 k) (*.f64 t (/.f64 (*.f64 t (sin.f64 k)) l)))
210.0ms
(/.f64 (*.f64 t (sin.f64 k)) l)
Compiler

Compiled 4337 to 3085 computations (28.9% saved)

simplify135.0ms (0.5%)

Algorithm
1×egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
049926173
149926173

prune285.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New2055210
Fresh369
Picked101
Done000
Total20911220
Error
5.6b
Counts
220 → 11
Compiler

Compiled 6386 to 2499 computations (60.9% saved)

regimes3.8s (12.7%)

Accuracy

Total 3.4b remaining (35.9%)

Threshold costs 0b (0%)

Compiler

Compiled 36964 to 27020 computations (26.9% saved)

bsearch187.0ms (0.6%)

Steps
ItersRangePoint
7
2.8307349104381136e-58
3.769604545828546e-56
1.0020146246906027e-57
7
-4.2005592757478343e-125
-1.6027264976540202e-126
-4.070589350152749e-125
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
053141
153141

end0.0ms (0%)

sample10.0s (33.6%)

Algorithm
1×intervals
Results
1.7s2739×body1024valid
554.0ms1226×body512valid
541.0ms3454×body128valid
209.0ms1403×body128invalid
182.0ms572×body256valid
60.0ms139×body512invalid
35.0ms58×body1024invalid
31.0ms103×body256invalid
7.0ms9×body2048valid
Compiler

Compiled 6138 to 4468 computations (27.2% saved)

Profiling

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