Details

Time bar (total: 5.2m)

sample525.0ms

Algorithm
intervals
Results
164.0ms49×body1280valid
94.0ms48×body640valid
63.0ms140×body80valid
27.0ms22×body320valid
23.0ms55×body80nan
9.0ms12×body160valid

simplify290.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
289.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.1b

localize41.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (fma 2 x (fma F F 2)) -1/2)
7.0b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.2b
(/ x (tan B))
0.2b
(/ (sin B) F)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
181×times-frac
106×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
45×unpow-prod-down
22×add-exp-log
19×associate-/r*
15×sqr-pow
13×add-cbrt-cube associate-/l*
11×div-exp div-inv
5×pow1 cbrt-undiv
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-to-exp pow-unpow clear-num frac-2neg pow-exp
2×associate-/r/
1×pow-pow tan-quot
Counts
4 → 214
Calls
4 calls:
Slowest
8.0ms
(/ (sin B) F)
8.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
5.0ms
(/ x (tan B))
4.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series691.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
233.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
230.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
172.0ms
(/ x (tan B))
55.0ms
(/ (sin B) F)

simplify53.6s

Counts
278 → 226
Calls
278 calls:
Slowest
798.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (cbrt (/ (sin B) F)))
675.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
637.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
633.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
609.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (sqrt (sin B)) 1))

prune3.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.9b

localize59.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (fma 2 x (fma F F 2)) -1/2)
17.3b
(pow (fma 2 x (fma F F 2)) -1/2)
0.6b
(* (/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (sin B)) (/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (/ 1 F)))
0.4b
(sqrt (pow (fma 2 x (fma F F 2)) -1/2))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
402×times-frac
376×add-sqr-sqrt
203×sqrt-prod
160×*-un-lft-identity
140×add-cube-cbrt
135×associate-*r*
86×unpow-prod-down
65×unswap-sqr
48×sqr-pow
41×add-exp-log
34×associate-*l*
25×add-cbrt-cube
17×div-exp
12×div-inv
10×prod-exp
9×cbrt-undiv
8×pow1
6×pow-unpow cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square
2×pow-to-exp rec-exp pow-pow 1-exp pow-exp
1×frac-times sqrt-pow1 pow1/2 pow-prod-down associate-*l/ associate-*r/ associate-/r/ *-commutative
Counts
4 → 327
Calls
4 calls:
Slowest
45.0ms
(* (/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (sin B)) (/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (/ 1 F)))
5.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
5.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
2.0ms
(sqrt (pow (fma 2 x (fma F F 2)) -1/2))

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
285.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
269.0ms
(sqrt (pow (fma 2 x (fma F F 2)) -1/2))
264.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
234.0ms
(* (/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (sin B)) (/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (/ 1 F)))

simplify1.6m

Counts
355 → 339
Calls
355 calls:
Slowest
690.0ms
(/ (sqrt (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) (/ 1 (sqrt F)))
688.0ms
(- (+ (* 5/32 (/ (exp (* 1/4 (+ (log (/ 1 x)) (log 1/2)))) (pow x 2))) (exp (* 1/4 (+ (log (/ 1 x)) (log 1/2))))) (* 1/4 (/ (exp (* 1/4 (+ (log (/ 1 x)) (log 1/2)))) x)))
662.0ms
(* (/ (* (* (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (sqrt (pow (fma 2 x (fma F F 2)) -1/2))) (sqrt (pow (fma 2 x (fma F F 2)) -1/2))) (* (* (sin B) (sin B)) (sin B))) (/ (* (* (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (sqrt (pow (fma 2 x (fma F F 2)) -1/2))) (sqrt (pow (fma 2 x (fma F F 2)) -1/2))) (/ (* (* 1 1) 1) (* (* F F) F))))
644.0ms
(* (/ (* (* (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (sqrt (pow (fma 2 x (fma F F 2)) -1/2))) (sqrt (pow (fma 2 x (fma F F 2)) -1/2))) (* (* (sin B) (sin B)) (sin B))) (/ (* (* (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (sqrt (pow (fma 2 x (fma F F 2)) -1/2))) (sqrt (pow (fma 2 x (fma F F 2)) -1/2))) (* (* (/ 1 F) (/ 1 F)) (/ 1 F))))
630.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune6.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 9.9b

localize56.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (fma 2 x (fma F F 2)) -1/2)
17.3b
(pow (fma 2 x (fma F F 2)) -1/2)
0.4b
(sqrt (pow (fma 2 x (fma F F 2)) -1/2))
0.4b
(sqrt (pow (fma 2 x (fma F F 2)) -1/2))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×unpow-prod-down sqrt-prod
12×*-un-lft-identity add-cube-cbrt
6×pow1 rem-sqrt-square pow-unpow add-exp-log sqr-pow
4×expm1-log1p-u add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
2×pow-to-exp pow-pow sqrt-pow1 pow1/2 pow-exp
Counts
4 → 84
Calls
4 calls:
Slowest
8.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
2.0ms
(sqrt (pow (fma 2 x (fma F F 2)) -1/2))
2.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
2.0ms
(sqrt (pow (fma 2 x (fma F F 2)) -1/2))

series1.2s

Counts
4 → 12
Calls
4 calls:
Slowest
311.0ms
(sqrt (pow (fma 2 x (fma F F 2)) -1/2))
305.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
299.0ms
(sqrt (pow (fma 2 x (fma F F 2)) -1/2))
289.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

simplify6.3s

Counts
48 → 96
Calls
48 calls:
Slowest
606.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
536.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
481.0ms
(- (+ (* 5/8 (* (pow x 2) (pow 1/512 1/4))) (pow 1/2 1/4)) (* 1/2 (* x (pow 1/32 1/4))))
359.0ms
(- (+ (* 5/8 (* (pow x 2) (pow 1/512 1/4))) (pow 1/2 1/4)) (* 1/2 (* x (pow 1/32 1/4))))
310.0ms
(sqrt (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2))

prune1.9s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 9.9b

localize101.0ms

Local error

Found 4 expressions with local error:

17.3b
(pow (fma 2 x (fma F F 2)) -1/2)
1.5b
(* (* (/ (cbrt F) (cbrt (sin B))) (/ (cbrt F) (cbrt (sin B)))) (/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (cbrt (sin B)) (cbrt F))))
0.6b
(cbrt F)
0.6b
(cbrt F)

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
559×times-frac
302×add-sqr-sqrt
285×associate-*r*
270×cbrt-prod
264×*-un-lft-identity add-cube-cbrt
166×add-exp-log
128×unpow-prod-down
73×div-exp
63×prod-exp
46×sqr-pow
39×add-cbrt-cube
27×cbrt-undiv cbrt-unprod
16×unswap-sqr
11×pow-to-exp pow-exp
10×pow1
8×div-inv
5×frac-times associate-*l/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow-unpow pow-prod-down associate-*r/
2×pow1/3
1×pow-pow associate-*l* associate-/r/ *-commutative
Counts
4 → 420
Calls
4 calls:
Slowest
69.0ms
(* (* (/ (cbrt F) (cbrt (sin B))) (/ (cbrt F) (cbrt (sin B)))) (/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (cbrt (sin B)) (cbrt F))))
3.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms
(cbrt F)
1.0ms
(cbrt F)

series1.1s

Counts
4 → 12
Calls
4 calls:
Slowest
327.0ms
(cbrt F)
294.0ms
(cbrt F)
261.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
234.0ms
(* (* (/ (cbrt F) (cbrt (sin B))) (/ (cbrt F) (cbrt (sin B)))) (/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (cbrt (sin B)) (cbrt F))))

simplify1.9m

Counts
405 → 432
Calls
405 calls:
Slowest
922.0ms
(+ (+ (log (/ (cbrt F) (cbrt (sin B)))) (- (log (cbrt F)) (log (cbrt (sin B))))) (- (* (log (fma 2 x (fma F F 2))) -1/2) (- (log (cbrt (sin B))) (log (cbrt F)))))
780.0ms
(* (* (* (* (/ (cbrt F) (cbrt (sin B))) (/ (cbrt F) (cbrt (sin B)))) (/ (cbrt F) (cbrt (sin B)))) (* (* (/ (cbrt F) (cbrt (sin B))) (/ (cbrt F) (cbrt (sin B)))) (/ (cbrt F) (cbrt (sin B))))) (/ (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (* (* (/ (cbrt (sin B)) (cbrt F)) (/ (cbrt (sin B)) (cbrt F))) (/ (cbrt (sin B)) (cbrt F)))))
768.0ms
(* (* (/ F (sin B)) (* (* (/ (cbrt F) (cbrt (sin B))) (/ (cbrt F) (cbrt (sin B)))) (/ (cbrt F) (cbrt (sin B))))) (/ (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (* (* (/ (cbrt (sin B)) (cbrt F)) (/ (cbrt (sin B)) (cbrt F))) (/ (cbrt (sin B)) (cbrt F)))))
731.0ms
(* (* (* (* (/ (cbrt F) (cbrt (sin B))) (/ (cbrt F) (cbrt (sin B)))) (/ (cbrt F) (cbrt (sin B)))) (* (* (/ (cbrt F) (cbrt (sin B))) (/ (cbrt F) (cbrt (sin B)))) (/ (cbrt F) (cbrt (sin B))))) (* (* (/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (cbrt (sin B)) (cbrt F))) (/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (cbrt (sin B)) (cbrt F)))) (/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (cbrt (sin B)) (cbrt F)))))
722.0ms
(* (* (* (* (/ (cbrt F) (cbrt (sin B))) (/ (cbrt F) (cbrt (sin B)))) (/ (cbrt F) (cbrt (sin B)))) (/ F (sin B))) (/ (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (* (* (/ (cbrt (sin B)) (cbrt F)) (/ (cbrt (sin B)) (cbrt F))) (/ (cbrt (sin B)) (cbrt F)))))

prune9.0s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

regimes423.0ms

Accuracy

94.1% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 10.5b

bsearch523.0ms

end0.0ms

sample14.7s

Algorithm
intervals
Results
6.1s1744×body1280valid
3.7s1363×body640valid
2.3s4754×body80valid
1.0s642×body320valid
788.0ms1557×body80nan
363.0ms363×body160valid