Details

Time bar (total: 2.6m)

sample4.8s

Algorithm
intervals
Results
4.6s1118×body10240exit
78.0ms66×body1280valid
47.0ms55×body640valid
33.0ms206×body80valid
12.0ms21×body320valid
5.0ms15×body160valid

simplify29.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
04813
116113
294413
3500212

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 35.0b

localize25.0ms

Local error

Found 4 expressions with local error:

2.2b
(* (pow t 3.0) (sin k))
3.4b
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
6.1b
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
29.1b
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
73×times-frac
56×add-sqr-sqrt
50×div-exp
41×add-cube-cbrt *-un-lft-identity
40×prod-exp
33×associate-*l*
30×cbrt-undiv
22×cbrt-unprod
11×div-inv
10×associate-*r*
8×associate-/l*
7×unswap-sqr
6×pow1 associate-/r*
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
2×tan-quot frac-2neg clear-num associate-/r/ *-commutative sqr-pow
1×frac-times associate-*r/ pow-prod-down associate-*l/ associate-/l/
Counts
4 → 184
Calls
4 calls:
6.0ms
(* (pow t 3.0) (sin k))
8.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
4.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
30.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

series1.4s

Counts
4 → 12
Calls
4 calls:
166.0ms
(* (pow t 3.0) (sin k))
322.0ms
(/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k))
69.0ms
(/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0)))
846.0ms
(* (/ (/ 2.0 (* (pow t 3.0) (sin k))) (tan k)) (/ (* l l) (fma 2 1.0 (pow (/ k t) 2.0))))

simplify49.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
010192396
150011978

prune711.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 28.3b

localize20.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
2.2b
(* (pow t 3.0) (sin k))
6.8b
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
20.5b
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
117×add-exp-log
74×add-cbrt-cube
49×prod-exp
41×div-exp
33×add-sqr-sqrt
27×cbrt-unprod
25×cbrt-undiv
22×associate-*l*
21×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*r*
8×pow1
6×unswap-sqr
5×pow-to-exp pow-exp
4×expm1-log1p-u unpow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-/r* *-commutative
2×tan-quot pow-prod-down associate-/r/ sqr-pow
1×frac-times frac-2neg associate-*r/ clear-num associate-/l/ associate-/l*
Counts
4 → 150
Calls
4 calls:
11.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
6.0ms
(* (pow t 3.0) (sin k))
14.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
47.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.8s

Counts
4 → 12
Calls
4 calls:
453.0ms
(/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k))
172.0ms
(* (pow t 3.0) (sin k))
341.0ms
(* (/ 2.0 (* (pow t 3.0) (sin k))) l)
869.0ms
(* (/ (* (/ 2.0 (* (pow t 3.0) (sin k))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify125.0ms

Algorithm
egg-herbie
Counts
162 → 162
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09131905
148941506
250011506

prune595.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 27.5b

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (* (/ 2.0 (* (pow t (/ 3.0 2)) (* (pow t (/ 3.0 2)) (sin k)))) l) (tan k))
3.5b
(* (pow t (/ 3.0 2)) (sin k))
6.8b
(* (/ 2.0 (* (pow t (/ 3.0 2)) (* (pow t (/ 3.0 2)) (sin k)))) l)
20.5b
(* (/ (* (/ 2.0 (* (pow t (/ 3.0 2)) (* (pow t (/ 3.0 2)) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite191.0ms

Algorithm
rewrite-expression-head
Rules
327×add-exp-log
175×prod-exp
113×div-exp
100×add-cbrt-cube
41×cbrt-unprod
33×cbrt-undiv add-sqr-sqrt
29×pow-to-exp pow-exp
22×associate-*l*
21×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*r*
8×pow1
6×unswap-sqr
4×expm1-log1p-u unpow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-*l/ associate-/r* *-commutative
2×tan-quot pow-prod-down associate-/r/ sqr-pow
1×frac-times frac-2neg associate-*r/ clear-num associate-/l/ associate-/l*
Counts
4 → 190
Calls
4 calls:
30.0ms
(/ (* (/ 2.0 (* (pow t (/ 3.0 2)) (* (pow t (/ 3.0 2)) (sin k)))) l) (tan k))
6.0ms
(* (pow t (/ 3.0 2)) (sin k))
35.0ms
(* (/ 2.0 (* (pow t (/ 3.0 2)) (* (pow t (/ 3.0 2)) (sin k)))) l)
109.0ms
(* (/ (* (/ 2.0 (* (pow t (/ 3.0 2)) (* (pow t (/ 3.0 2)) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series2.0s

Counts
4 → 12
Calls
4 calls:
455.0ms
(/ (* (/ 2.0 (* (pow t (/ 3.0 2)) (* (pow t (/ 3.0 2)) (sin k)))) l) (tan k))
173.0ms
(* (pow t (/ 3.0 2)) (sin k))
362.0ms
(* (/ 2.0 (* (pow t (/ 3.0 2)) (* (pow t (/ 3.0 2)) (sin k)))) l)
1.0s
(* (/ (* (/ 2.0 (* (pow t (/ 3.0 2)) (* (pow t (/ 3.0 2)) (sin k)))) l) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify59.0ms

Algorithm
egg-herbie
Counts
202 → 202
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010733131
150012332

prune620.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 17.3b

localize28.0ms

Local error

Found 4 expressions with local error:

2.2b
(/ (* (/ 1 (pow t (/ 3.0 2))) (* (/ 2.0 (* (pow t (/ 3.0 2)) (sin k))) l)) (tan k))
3.5b
(* (pow t (/ 3.0 2)) (sin k))
9.2b
(* (/ 2.0 (* (pow t (/ 3.0 2)) (sin k))) l)
20.5b
(* (/ (* (/ 1 (pow t (/ 3.0 2))) (* (/ 2.0 (* (pow t (/ 3.0 2)) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
1089×add-exp-log
555×prod-exp
477×div-exp
173×add-cbrt-cube
86×pow-to-exp pow-exp
73×cbrt-unprod
63×cbrt-undiv
54×rec-exp 1-exp
33×add-sqr-sqrt
22×associate-*l*
21×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*r*
8×pow1
6×unswap-sqr
5×associate-*l/
4×expm1-log1p-u unpow-prod-down log1p-expm1-u div-inv add-log-exp
3×associate-/r* *-commutative associate-/l/
2×tan-quot frac-times associate-*r/ pow-prod-down associate-/r/ sqr-pow
1×frac-2neg clear-num associate-/l*
Counts
4 → 332
Calls
4 calls:
36.0ms
(/ (* (/ 1 (pow t (/ 3.0 2))) (* (/ 2.0 (* (pow t (/ 3.0 2)) (sin k))) l)) (tan k))
6.0ms
(* (pow t (/ 3.0 2)) (sin k))
15.0ms
(* (/ 2.0 (* (pow t (/ 3.0 2)) (sin k))) l)
130.0ms
(* (/ (* (/ 1 (pow t (/ 3.0 2))) (* (/ 2.0 (* (pow t (/ 3.0 2)) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

series1.9s

Counts
4 → 12
Calls
4 calls:
459.0ms
(/ (* (/ 1 (pow t (/ 3.0 2))) (* (/ 2.0 (* (pow t (/ 3.0 2)) (sin k))) l)) (tan k))
175.0ms
(* (pow t (/ 3.0 2)) (sin k))
344.0ms
(* (/ 2.0 (* (pow t (/ 3.0 2)) (sin k))) l)
876.0ms
(* (/ (* (/ 1 (pow t (/ 3.0 2))) (* (/ 2.0 (* (pow t (/ 3.0 2)) (sin k))) l)) (tan k)) (/ l (fma 2 1.0 (pow (/ k t) 2.0))))

simplify84.0ms

Algorithm
egg-herbie
Counts
344 → 344
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
016265957
150014972

prune563.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 15.2b

regimes311.0ms

Accuracy

55.4% (2.6b remaining)

Error of 17.8b against oracle of 15.1b and baseline of 21.0b

bsearch1.7s

Steps
ItersRangePoint
8
3.921738219708347e-40
1.717676287332507e-37
1.6050627599136617e-37
6
1.2492776414848108e-136
1.563938040732864e-135
1.669992605686442e-136

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05753
16153
26153

end0.0ms

sample2.3m

Algorithm
intervals
Results
2.2m33177×body10240exit
2.3s2045×body1280valid
1.4s1804×body640valid
1.0s5901×body80valid
423.0ms804×body320valid
161.0ms421×body160valid