Details

Time bar (total: 14.9s)

analyze2.1s (14.4%)

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)

sample133.0ms (0.9%)

Algorithm
1×intervals
Results
57.0ms73×body1280valid
34.0ms54×body640valid
14.0ms105×body80valid
5.0ms13×body320valid
4.0ms33×body80invalid
3.0ms11×body160valid
1.0ms3×body320invalid
1.0ms2×body640invalid
1.0ms1×body1280invalid
0.0ms1×body160invalid
Compiler

Compiled 51 to 46 computations (9.8% saved)

simplify123.0ms (0.8%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (108.0ms)

IterNodesCost
0493235
1493235

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 33.2b

Counts
2 → 1
Compiler

Compiled 46 to 38 computations (17.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.8b
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
2.9b
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
13.9b
(*.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)))
16.8b
(/.f64 (pow.f64 t 3) (*.f64 l l))

rewrite76.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
108×add-exp-log_binary64
58×prod-exp_binary64
52×add-cbrt-cube_binary64
28×times-frac_binary64
26×cbrt-unprod_binary64 add-sqr-sqrt_binary64
24×div-exp_binary64
20×pow1_binary64
19×*-un-lft-identity_binary64
18×associate-*l*_binary64
17×add-cube-cbrt_binary64
16×associate-*l/_binary64
12×associate-/l*_binary64
10×pow-prod-down_binary64 associate-*r*_binary64 unpow-prod-down_binary64 cube-prod_binary64 frac-times_binary64
8×pow-to-exp_binary64 cbrt-undiv_binary64 pow-exp_binary64 tan-quot_binary64
6×associate-*r/_binary64
5×unswap-sqr_binary64
4×flip3-+_binary64 add-log-exp_binary64 sqr-pow_binary64 insert-posit16 flip-+_binary64
3×unpow3_binary64 *-commutative_binary64 cube-mult_binary64
2×div-inv_binary64
1×associate-/r*_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64
Counts
4 → 163
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)))
16.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
13.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
9.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

series1.1s (7.7%)

Counts
4 → 12
Calls

4 calls:

658.0ms
(*.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)))
308.0ms
(*.f64 (*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k)) (tan.f64 k))
128.0ms
(*.f64 (/.f64 (pow.f64 t 3) (*.f64 l l)) (sin.f64 k))
55.0ms
(/.f64 (pow.f64 t 3) (*.f64 l l))

simplify103.0ms (0.7%)

Algorithm
1×egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
055553762

prune292.0ms (2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New16312175
Fresh000
Picked101
Done000
Total16412176

Merged error: 14.6b

Counts
176 → 12
Compiler

Compiled 5187 to 2869 computations (44.7% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
4.2b
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
7.8b
(/.f64 (*.f64 t t) l)
13.9b
(*.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)))

rewrite77.0ms (0.5%)

Algorithm
1×rewrite-expression-head
Rules
113×add-exp-log_binary64 add-cbrt-cube_binary64
65×cbrt-unprod_binary64 prod-exp_binary64
44×associate-*l/_binary64
34×frac-times_binary64
29×pow1_binary64
20×cbrt-undiv_binary64 div-exp_binary64
17×pow-prod-down_binary64
16×tan-quot_binary64
15×add-sqr-sqrt_binary64
14×associate-*r/_binary64
13×*-un-lft-identity_binary64
11×add-cube-cbrt_binary64
10×associate-*r*_binary64
9×associate-*l*_binary64
8×flip3-+_binary64 flip-+_binary64
7×times-frac_binary64
4×add-log-exp_binary64 insert-posit16
3×associate-/r*_binary64 *-commutative_binary64
2×unswap-sqr_binary64 div-inv_binary64
1×distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64 associate-/l*_binary64
Counts
4 → 155
Calls

4 calls:

33.0ms
(*.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)))
18.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
10.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
6.0ms
(/.f64 (*.f64 t t) l)

series1.1s (7.4%)

Counts
4 → 12
Calls

4 calls:

651.0ms
(*.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)))
313.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))) (tan.f64 k))
112.0ms
(*.f64 (/.f64 (*.f64 t t) l) (sin.f64 k))
28.0ms
(/.f64 (*.f64 t t) l)

simplify187.0ms (1.3%)

Algorithm
1×egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 0 (136.0ms)

IterNodesCost
049654091
149654091

prune247.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New1607167
Fresh5611
Picked101
Done000
Total16613179

Merged error: 9.7b

Counts
179 → 13
Compiler

Compiled 5123 to 2589 computations (49.5% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b
(/.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))))
2.8b
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
4.3b
(*.f64 (/.f64 t l) (sin.f64 k))
13.9b
(*.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)))

rewrite154.0ms (1%)

Algorithm
1×rewrite-expression-head
Rules
421×add-exp-log_binary64
304×add-cbrt-cube_binary64
259×prod-exp_binary64
181×cbrt-unprod_binary64
179×frac-times_binary64
178×associate-*l/_binary64
108×div-exp_binary64
81×associate-*r/_binary64
69×cbrt-undiv_binary64
56×tan-quot_binary64
47×associate-/r/_binary64
40×pow1_binary64
32×flip3-+_binary64 flip-+_binary64
26×pow-prod-down_binary64
21×add-sqr-sqrt_binary64
18×*-un-lft-identity_binary64 1-exp_binary64
16×add-cube-cbrt_binary64
15×associate-*l*_binary64
13×times-frac_binary64
10×associate-*r*_binary64
4×add-log-exp_binary64 insert-posit16
3×associate-/l*_binary64 *-commutative_binary64
2×unswap-sqr_binary64 div-inv_binary64
1×associate-/r*_binary64 distribute-lft-out_binary64 distribute-lft-in_binary64 distribute-rgt-in_binary64 clear-num_binary64 frac-2neg_binary64
Counts
4 → 312
Calls

4 calls:

43.0ms
(/.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))))
42.0ms
(*.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)))
24.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.6s (10.6%)

Counts
4 → 12
Calls

4 calls:

656.0ms
(*.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)))
495.0ms
(/.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))))
321.0ms
(*.f64 (*.f64 (/.f64 t l) (*.f64 (/.f64 t 1) (*.f64 (/.f64 t l) (sin.f64 k)))) (tan.f64 k))
107.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify241.0ms (1.6%)

Algorithm
1×egg-herbie
Counts
324 → 324
Iterations

Useful iterations: 0 (142.0ms)

IterNodesCost
049709974
149709974

prune575.0ms (3.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New3159324
Fresh7512
Picked101
Done000
Total32314337

Merged error: 7.8b

Counts
337 → 14
Compiler

Compiled 10040 to 5340 computations (46.8% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.1b
(/.f64 (/.f64 l t) (*.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))
4.3b
(*.f64 (/.f64 t l) (sin.f64 k))
14.1b
(/.f64 (/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))

rewrite95.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
231×times-frac_binary64
130×*-un-lft-identity_binary64
125×add-exp-log_binary64 add-cbrt-cube_binary64
93×add-sqr-sqrt_binary64
88×add-cube-cbrt_binary64
47×cbrt-unprod_binary64 cbrt-undiv_binary64 prod-exp_binary64 div-exp_binary64
33×associate-/l*_binary64
22×associate-*l/_binary64
21×distribute-lft-out_binary64 associate-*r/_binary64
20×associate-/r/_binary64
15×pow1_binary64 div-inv_binary64
14×associate-*l*_binary64 tan-quot_binary64
7×pow-prod-down_binary64 frac-times_binary64
6×associate-*r*_binary64
5×associate-/r*_binary64
4×add-log-exp_binary64 insert-posit16
2×associate-/l/_binary64 unswap-sqr_binary64 clear-num_binary64 frac-2neg_binary64 *-commutative_binary64
1×flip3-+_binary64 flip-+_binary64
Counts
4 → 262
Calls

4 calls:

33.0ms
(/.f64 (/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
19.0ms
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
17.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
8.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

series1.1s (7.7%)

Counts
4 → 12
Calls

4 calls:

391.0ms
(/.f64 (/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))) (+.f64 2 (pow.f64 (/.f64 k t) 2)))
348.0ms
(/.f64 (/.f64 l t) (*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k)))
300.0ms
(*.f64 (*.f64 t (*.f64 (/.f64 t l) (sin.f64 k))) (tan.f64 k))
105.0ms
(*.f64 (/.f64 t l) (sin.f64 k))

simplify226.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
274 → 274
Iterations

Useful iterations: 0 (138.0ms)

IterNodesCost
049749327
149749327

prune369.0ms (2.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New2695274
Fresh6713
Picked101
Done000
Total27612288

Merged error: 7.8b

Counts
288 → 12
Compiler

Compiled 9012 to 3217 computations (64.3% saved)

regimes175.0ms (1.2%)

Compiler

Compiled 1256 to 983 computations (21.7% saved)

bsearch222.0ms (1.5%)

Steps
ItersRangePoint
4
8.405344737118046e-91
1.3941008129790041e-90
9.599619134737473e-91
11
-5.789347091598093e-173
-1.5343064342281768e-195
-1.192768194971382e-191
Compiler

Compiled 1 to 3 computations (-200% saved)

simplify10.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
058112
158112

end0.0ms (0%)

sample4.4s (29.3%)

Algorithm
1×intervals
Results
1.7s2104×body1280valid
857.0ms1584×body640valid
434.0ms3226×body80valid
299.0ms743×body320valid
182.0ms1357×body80invalid
97.0ms343×body160valid
71.0ms131×body640invalid
49.0ms119×body320invalid
22.0ms25×body1280invalid
15.0ms58×body160invalid
Compiler

Compiled 399 to 304 computations (23.8% saved)

Profiling

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