Details

Time bar (total: 2.4m)

sample777.0ms

Algorithm
intervals
Results
165.0ms169×body80valid
137.0ms47×body1280valid
124.0ms42×body640valid
35.0ms19×body320valid
24.0ms54×body80nan
9.0ms11×body160valid

simplify746.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
745.0ms
(+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2)))))

prune52.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.0b

localize74.0ms

Local error

Found 4 expressions with local error:

19.6b
(pow (fma 2 x (fma F F 2)) -1/2)
10.1b
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.1b
(/ (sin B) F)
0.1b
(/ x (tan B))

rewrite59.0ms

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
17.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
16.0ms
(/ (sin B) F)
10.0ms
(/ x (tan B))
7.0ms
(pow (fma 2 x (fma F F 2)) -1/2)

series852.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
383.0ms
(pow (fma 2 x (fma F F 2)) -1/2)
236.0ms
(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
180.0ms
(/ x (tan B))
54.0ms
(/ (sin B) F)

simplify52.6s

Counts
278 → 226
Calls
278 calls:
Slowest
641.0ms
(/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (/ (sqrt (sin B)) F))
636.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
615.0ms
(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
614.0ms
(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
603.0ms
(/ (pow (cbrt (fma 2 x (fma F F 2))) -1/2) (/ (sqrt (sin B)) (sqrt F)))

prune3.3s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.5b

localize84.0ms

Local error

Found 4 expressions with local error:

19.6b
(pow (fma x 2 (fma F F 2)) -1/2)
0.9b
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.2b
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.1b
(/ 1 (sin B))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
58×add-exp-log
31×prod-exp
29×add-sqr-sqrt
24×*-un-lft-identity add-cube-cbrt
20×add-cbrt-cube associate-*l*
18×times-frac
10×div-exp
8×pow1
7×unpow-prod-down cbrt-unprod
6×pow-to-exp pow-exp
5×rec-exp 1-exp
4×expm1-log1p-u associate-*r* insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow associate-/r* associate-/l* unswap-sqr sqr-pow
2×*-commutative div-inv
1×clear-num pow-pow frac-2neg pow-prod-down associate-*l/ pow-flip inv-pow
Counts
4 → 129
Calls
4 calls:
Slowest
51.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
17.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
11.0ms
(/ 1 (sin B))
4.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series589.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
290.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
151.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
122.0ms
(* (pow (fma x 2 (fma F F 2)) -1/2) F)
25.0ms
(/ 1 (sin B))

simplify12.8s

Counts
97 → 141
Calls
97 calls:
Slowest
618.0ms
(- (+ (* 3/2 (* (sqrt 1/32) (* (pow x 2) F))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))
524.0ms
(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))
487.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
484.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
468.0ms
(+ (- (log 1) (log (sin B))) (log (* (pow (fma x 2 (fma F F 2)) -1/2) F)))

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.5b

localize76.0ms

Local error

Found 4 expressions with local error:

19.6b
(pow (fma x 2 (fma F F 2)) -1/2)
0.4b
(* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2))
0.2b
(* (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2)) F)
0.1b
(/ 1 (sin B))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
69×add-exp-log
42×add-sqr-sqrt
37×prod-exp
27×*-un-lft-identity
24×times-frac add-cube-cbrt
20×add-cbrt-cube
14×div-exp associate-*l*
10×associate-*r*
9×pow-to-exp unpow-prod-down pow-exp unswap-sqr
8×pow1
7×rec-exp 1-exp cbrt-unprod
5×sqr-pow
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow-unpow associate-/r* associate-*l/ associate-/l*
2×*-commutative div-inv
1×clear-num pow-pow frac-2neg pow-prod-down pow-flip inv-pow
Counts
4 → 142
Calls
4 calls:
Slowest
33.0ms
(* (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2)) F)
16.0ms
(* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2))
5.0ms
(/ 1 (sin B))
2.0ms
(pow (fma x 2 (fma F F 2)) -1/2)

series546.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
260.0ms
(pow (fma x 2 (fma F F 2)) -1/2)
149.0ms
(* (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2)) F)
119.0ms
(* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2))
18.0ms
(/ 1 (sin B))

simplify17.4s

Counts
118 → 154
Calls
118 calls:
Slowest
603.0ms
(* (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))) (* (* (pow (fma x 2 (fma F F 2)) -1/2) (pow (fma x 2 (fma F F 2)) -1/2)) (pow (fma x 2 (fma F F 2)) -1/2)))
590.0ms
(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
559.0ms
(* (sqrt (/ 1 (sin B))) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
540.0ms
(* (sqrt (/ 1 (sin B))) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
507.0ms
(+ (log (* (/ 1 (sin B)) (pow (fma x 2 (fma F F 2)) -1/2))) (log F))

prune2.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 9.5b

localize54.0ms

Local error

Found 4 expressions with local error:

20.2b
(pow (fma x 2 (fma F F 2)) (/ -1/2 2))
20.2b
(pow (fma x 2 (fma F F 2)) (/ -1/2 2))
0.6b
(* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2)))
0.4b
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
120×add-exp-log
85×prod-exp
51×add-sqr-sqrt
36×*-un-lft-identity
35×add-cube-cbrt
32×pow-to-exp pow-exp
29×times-frac
26×pow-unpow
24×unpow-prod-down
20×div-exp associate-*l*
18×add-cbrt-cube
12×unswap-sqr sqr-pow
10×rec-exp 1-exp
8×pow1 associate-*r*
7×swap-sqr cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×div-inv
2×cbrt-undiv pow-pow pow-prod-down *-commutative
1×pow2 associate-*l/ pow-sqr pow-prod-up
Counts
4 → 189
Calls
4 calls:
Slowest
43.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2))))
27.0ms
(* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2)))
4.0ms
(pow (fma x 2 (fma F F 2)) (/ -1/2 2))
3.0ms
(pow (fma x 2 (fma F F 2)) (/ -1/2 2))

series847.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
320.0ms
(pow (fma x 2 (fma F F 2)) (/ -1/2 2))
307.0ms
(pow (fma x 2 (fma F F 2)) (/ -1/2 2))
128.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2))))
92.0ms
(* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2)))

simplify30.6s

Counts
173 → 201
Calls
173 calls:
Slowest
622.0ms
(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2))))
545.0ms
(* (pow (fma x 2 (fma F F 2)) (/ -1/2 2)) (pow (fma x 2 (fma F F 2)) (/ -1/2 2)))
511.0ms
(+ (- 0 (log (sin B))) (+ (* (log (fma x 2 (fma F F 2))) (/ -1/2 2)) (* (log (fma x 2 (fma F F 2))) (/ -1/2 2))))
507.0ms
(* (sqrt (/ 1 (sin B))) (pow (fma x 2 (fma F F 2)) (/ -1/2 2)))
495.0ms
(+ (- (log 1) (log (sin B))) (+ (* (log (fma x 2 (fma F F 2))) (/ -1/2 2)) (* (log (fma x 2 (fma F F 2))) (/ -1/2 2))))

prune3.5s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 9.5b

regimes545.0ms

Accuracy

0% (0.6b remaining)

Error of 10.2b against oracle of 9.6b and baseline of 10.2b

bsearch3.0ms

end0.0ms

sample14.7s

Algorithm
intervals
Results
5.8s1688×body1280valid
3.4s1411×body640valid
2.9s4800×body80valid
1.1s696×body320valid
695.0ms1657×body80nan
394.0ms346×body160valid